Section 2.6 Self Quiz

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
A ∨ (~A ⊃ A) / A

Valid correct incorrect

Invalid. Counterexample when A is true correct incorrect

Invalid. Counterexample when A is false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
B ⊃ ~B
~B / B

Valid correct incorrect

Invalid. Counterexample when B is true correct incorrect

Invalid. Counterexample when B is false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~C ⊃ D
D ⊃ C / C

Valid correct incorrect

Invalid. Counterexample when C and D are true correct incorrect

Invalid. Counterexample when C is true and D is false correct incorrect

Invalid. Counterexample when D is true and C is false correct incorrect

Invalid. Counterexample when C and D are true correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~E ∨ F
~F / E

Valid correct incorrect

Invalid. Counterexample when E and F are true correct incorrect

Invalid. Counterexample when E is true and F is false correct incorrect

Invalid. Counterexample when F is true and E is false correct incorrect

Invalid. Counterexample when E and F are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~G ⊃ H
~H / G

Valid correct incorrect

Invalid. Counterexample when G and H are true correct incorrect

Invalid. Counterexample when G is true and H is false correct incorrect

Invalid. Counterexample when H is true and G is false correct incorrect

Invalid. Counterexample when G and H are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
I ≡ ~J
I ∨ J / I

Valid correct incorrect

Invalid. Counterexample when I and J are true correct incorrect

Invalid. Counterexample when I is true and J is false correct incorrect

Invalid. Counterexample when J is true and I is false correct incorrect

Invalid. Counterexample when I and J are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~K ≡ L / (K · L) ∨ (K · ~L)

Valid correct incorrect

Invalid. Counterexample when K and L are true correct incorrect

Invalid. Counterexample when K is true and L is false correct incorrect

Invalid. Counterexample when L is true and K is false correct incorrect

Invalid. Counterexample when K and L are false correct incorrect

* not completed

. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~(M ≡ ~N)
M / N

Valid correct incorrect

Invalid. Counterexample when M and N are true correct incorrect

Invalid. Counterexample when M is true and N is false correct incorrect

Invalid. Counterexample when N is true and M is false correct incorrect

Invalid. Counterexample when M and N are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(O ≡ P) ∨ P / P ∨ ~O

Valid correct incorrect

Invalid. Counterexample when O and P are true correct incorrect

Invalid. Counterexample when O is true and P is false correct incorrect

Invalid. Counterexample when P is true and O is false correct incorrect

Invalid. Counterexample when O and P are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
Q ≡ R
~(S ∨ Q) / R

Valid correct incorrect

Invalid. Counterexample when Q and S are true and R is false correct incorrect

Invalid. Counterexample when Q is true and S and R are false correct incorrect

Invalid. Counterexample when S is true and Q and R are false correct incorrect

Invalid. Counterexample when Q, S, and R are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
T ∨ U
W · T / U

Valid correct incorrect

Invalid. Counterexample when T and W are true and U is false correct incorrect

Invalid. Counterexample when T is true and W and U are false correct incorrect

Invalid. Counterexample when W is true and T and U are false correct incorrect

Invalid. Counterexample when T, W, and U are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~X ⊃ Y
Y ⊃ Z
~Z / ~X

Valid correct incorrect

Invalid. Counterexample when X, Y, and Z are true correct incorrect

Invalid. Counterexample when Y and Z are true and Z is false correct incorrect

Invalid. Counterexample when Z and X are true and Y is false correct incorrect

Invalid. Counterexample when X is true and Y and Z are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~A · ~B
(A ∨ C) ∨ B / C

Valid correct incorrect

Invalid. Counterexample when A and B are true and C is false correct incorrect

Invalid. Counterexample when A is true and B and C are false correct incorrect

Invalid. Counterexample when B is true and A and C are false correct incorrect

Invalid. Counterexample when A, B, and C are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
D ⊃ (~E ⊃ F)
~D ⊃ E
~E / F

Valid correct incorrect

Invalid. Counterexample when D and E are true and F is false correct incorrect

Invalid. Counterexample when D is true and E and F are false correct incorrect

Invalid. Counterexample when E is true and D and F are false correct incorrect

Invalid. Counterexample when D, E, and F are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(G ≡ H) · ~I
~G ∨ (~H ∨ I) / G

Valid correct incorrect

Invalid. Counterexample when H and I are true and G is false correct incorrect

Invalid. Counterexample when H is true and I and G are false correct incorrect

Invalid. Counterexample when I is true and H and G are false correct incorrect

Invalid. Counterexample when H, I, and G are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
J ≡ ~K
J ∨ L
~K / L

Valid correct incorrect

Invalid. Counterexample when J and K are true and L is false correct incorrect

Invalid. Counterexample when J is true and K and L are false correct incorrect

Invalid. Counterexample when K is true and J and L are false correct incorrect

Invalid. Counterexample when J, K, and L are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
M ∨ N
~M · O / N

Valid correct incorrect

Invalid. Counterexample when M and O are true and N is false correct incorrect

Invalid. Counterexample when M is true and O and N are false correct incorrect

Invalid. Counterexample when O is true and M and N are false correct incorrect

Invalid. Counterexample when M, N, and O are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
P ⊃ Q
Q · R / ~P · R

Valid correct incorrect

Invalid. Counterexample when P, R, and Q are true correct incorrect

Invalid. Counterexample when P and Q are true and R is false correct incorrect

Invalid. Counterexample when R and Q are true and P is false correct incorrect

Invalid. Counterexample when Q is true and P and R are false correct incorrect

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. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~S ∨ T
~S · U
~T ∨ U / T · U

Valid correct incorrect

Invalid. Counterexample when S, T, and U are true correct incorrect

Invalid. Counterexample when S and U are true and T is false correct incorrect

Invalid. Counterexample when T and U are true and S is false correct incorrect

Invalid. Counterexample when U is true and S and T are false correct incorrect