Let p: it is cold, q: it is humid, and r: it is snowing. Which statement represents "It is cold and humid if and only if it is snowing"? (p ∨ q) ↔ r (p ↔ r) ∧ (q ↔ r) [ (p ∧ q) → r] ∧ [r → (p ∧ q) ] [ (p → r) ∧ (q → r) ] ∧ [ (r → p) ∧ (r → q) ]

Question

Mathematics

Thomas

20 June, 06:18

Let p: it is cold, q: it is humid, and r: it is snowing. Which statement represents "It is cold and humid if and only if it is snowing"? (p ∨ q) ↔ r (p ↔ r) ∧ (q ↔ r) [ (p ∧ q) → r] ∧ [r → (p ∧ q) ] [ (p → r) ∧ (q → r) ] ∧ [ (r → p) ∧ (r → q) ]

+1

Answers (2)

Know the Answer?

Abagail Dixon · Answer 1

Answer: the answer is c ...

Step-by-step explanation: if you're on edge2020 it's c

Kylan Myers · Answer 2

Answer: The answer is (b) [ (p∧q) ⇒r] ∧ [r⇒ (p∧q) ].

Step-by-step explanation: Given that The statements 'p', 'q' and 'r' are defined as follows.

p : it is cold,

q : it is humid,

r : it is snowing.

The statement 'it is cold and humid if and only if it is snowing' can be written as

(p∧q) ⇔ r.

We know that r ⇔ s can be written as (r⇒s) ∧ (s⇒r).

So, (p∧q) ⇔ r can be written as [ (p∧q) ⇒r] ∧ [r⇒ (p∧q) ].

Thus, the answer is (b) [ (p∧q) ⇒r] ∧ [r⇒ (p∧q) ].