Question

If p : It is raining, q : The weather is humid, which of the following statements are logically equivalent? Justify!
(i) If it is not raining then the weather is not humid.
(ii) It is raining if and only if the weather is humid.
(iii) It is not true that it is not raining or the weather is humid.
(iv) It is raining but the weather is not humid.
(v) The weather is humid only it it is raining.

Answer 1

p : It is raining, q : The weather is humid, which of the following statements are logically equivalent? Justify!
If it is not raining then the weather is not humid.