Section 3.10 Self Quiz

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. (A • B) ⊃ (C ∨ D)
2. A / C ∨ D

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. (E ∨ F) ⊃ (G • H)
2. E / G

Valid correct incorrect

Invalid. Counterexample when E, F, and H are true and G is false correct incorrect

Invalid. Counterexample when E and F are true and G and H are false correct incorrect

Invalid. Counterexample when E and H are true and F and G are false correct incorrect

Invalid. Counterexample when E is true and F, G, and H are false correct incorrect

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. (I ⊃ J) ⊃ K
2. I / K

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. (L ⊃ M) ⊃ N
2. M / N

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. A ⊃ B
2. C ⊃ D
3. ~A ⊃ C / B ∨ D

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. E ⊃ F
2. G ⊃ H
3. F ∨ H / E ∨ G

Valid correct incorrect

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

Invalid. Counterexample when F is true and E, G, and H are false correct incorrect

Invalid. Counterexample when E is true and F, G, and H are false correct incorrect

Invalid. Counterexample when F and G are true and E and H are false correct incorrect

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. A ⊃ (B • C)
2. C ⊃ (D ∨ A)
3. (~D ∨ E) ⊃ A / D

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. F ⊃ (G • H)
2. H ⊃ (I ∨ ~F)
3. (~I ∨ K) ⊃ F / I

Valid correct incorrect

Invalid. Counterexample when F, G, H, J, and K are true and I is false correct incorrect

Invalid. Counterexample when F, G, and J are true and H, I, and K are false correct incorrect

Invalid. Counterexample when G and K are true and F, H, I, and J are false correct incorrect

Invalid. Counterexample when F and H are true and G, I, J, and K are false correct incorrect

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. L ⊃ (M ∨ N)
2. N ⊃ (O ∨ ~L)
3. (L ∨ ~M) ⊃ N / ~L

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the argument is valid or invalid. If it is invalid, select a counterexample.
1. P ⊃ (~Q ∨ R)
2. Q ⊃ (S • ~R)
3. (Q ∨ T) ⊃ P / ~Q

Valid correct incorrect

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

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

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

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

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
(A • B) ∨ (A • ~B)

Logical truth correct incorrect

Not a logical truth. False valuation when A and B are true correct incorrect

Not a logical truth. False valuation when A is true and B is false correct incorrect

Not a logical truth. False valuation when B is true and A is false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
(C ∨ D) ∨ (C ∨ ~D)

Logical truth correct incorrect

Not a logical truth. False valuation when C and D are true correct incorrect

Not a logical truth. False valuation when C is true and D is false correct incorrect

Not a logical truth. False valuation when D is true and C is false correct incorrect

Not a logical truth. False valuation when C and D are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
(E ⊃ F) ∨ (F ⊃ E)

Logical truth correct incorrect

Not a logical truth. False valuation when E and F are true correct incorrect

Not a logical truth. False valuation when E is true and F is false correct incorrect

Not a logical truth. False valuation when F is true and E is false correct incorrect

Not a logical truth. False valuation when E and F are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
(G ≡ H) ∨ (~G ≡ H)

Logical truth correct incorrect

Not a logical truth. False valuation when G and H are true correct incorrect

Not a logical truth. False valuation when G is true and H is false correct incorrect

Not a logical truth. False valuation when H is true and G is false correct incorrect

Not a logical truth. False valuation when G and H are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
[(I ≡ J) • ~I] ⊃ ~J

Logical truth correct incorrect

Not a logical truth. False valuation when I and J are true correct incorrect

Not a logical truth. False valuation when I is true and J is false correct incorrect

Not a logical truth. False valuation when J is true and I is false correct incorrect

Not a logical truth. False valuation when I and J are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
[(K ≡ L) • ~K] ≡ ~L

Logical truth correct incorrect

Not a logical truth. False valuation when K and L are true correct incorrect

Not a logical truth. False valuation when K is true and L is false correct incorrect

Not a logical truth. False valuation when K is false and L is either true or false correct incorrect

Options B, C, and D, but not option A correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
[M ⊃ (N ∨ O)] ⊃ (M ⊃ N)

Logical truth correct incorrect

Not a logical truth. False valuation when M and O are true and N is false correct incorrect

Not a logical truth. False valuation when M is true and N and O are false correct incorrect

Not a logical truth. False valuation when N and O are true and M is false correct incorrect

Not a logical truth. False valuation when M, N, and O are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
[P ⊃ (Q • R)] ⊃ (P ⊃ Q)

Logical truth correct incorrect

Not a logical truth. False valuation when P and Q are true and R is false correct incorrect

Not a logical truth. False valuation when R is true and P and Q are false correct incorrect

Not a logical truth. False valuation when P and R are true and Q is false correct incorrect

Not a logical truth. False valuation when P is true and Q and R are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
[S ⊃ (T ∨ U)] ⊃ (~T ⊃ U)

Logical truth correct incorrect

Not a logical truth. False valuation when S, T, and U are true correct incorrect

Not a logical truth. False valuation when S and T are true and U is false correct incorrect

Not a logical truth. False valuation when S and U are true and T is false correct incorrect

Not a logical truth. False valuation when U is true and S and T are false correct incorrect

* not completed

. Determine whether the given proposition is a logical truth or not. If it is not a logical truth, select a false valuation.
[X ⊃ (Y ∨ Z)] ⊃ [(X ⊃ ~Y) ⊃ (X ⊃ Z)]

Logical truth correct incorrect

Not a logical truth. False valuation when X, Y, and Z are true correct incorrect

Not a logical truth. False valuation when X and Y are true and Z is false correct incorrect

Not a logical truth. False valuation when X and Z are true and Y is false correct incorrect

Not a logical truth. False valuation when X is true and Y and Z are false correct incorrect