Which of the following are valid logical arguments? (Select all that are.) (Q16) ?

A: p | q | r. Therefore, p | q.

B: p → q; !p. Therefore, !q.

C: (p | q) → r; p → !q; r. Therefore, q.

D: p → q; p ↔ r; r. Therefore, q.

Which of the following are valid logical arguments? (Select all that are.) (Q17) ?

A: p ↔ q; q. Therefore, p.

B: p → q. Therefore, p ↔ q.

C: r → (p | q); p → !q; r. Therefore, (p & !q) | (q & !p).

D: p → q; !q. Therefore, !p.

Which of the following are valid logical arguments? (Select all that are.) (Q18) ?

A: (p & q) | (!p & !q). Therefore, p → q.

B: (p & q) | r. Therefore, (p & r) | (q & r).

C: p → q. Therefore, (p & q) | (!p & !q).

D: (p & q) → r; !r. Therefore, !p | !q.

## Expert Answer

16. D p<—->r can be seen as r—->p and since p—->q then by associativity we can say that r—->q

17. A p<—->q becaucse this means p—>q and q—>p so hence q therefore p

18. (p & q) | r therefore (p&r) | (q&r) this is a distribution property of logical operators