Question

mathematical reasoning

Answer 1

your answer is ((a))

Answer 2

1.

$p \implies \neg q \equiv \top$

$\neg p \lor \neg q \equiv \top$

Atleast one of the not p and not q is true

2.

$\neg r \implies q \equiv \sf \top$

$r \lor q \equiv \top$

Atleast One of the r and q is true.

3.

$p \equiv \top$

Now, for 1 to be true, q must be False.

Now, for 2 to be true r must be true.

Therefore, the Answer is (2) r is true