Question

Let p: The day is Tuesday.

Let q: The day is Thursday.
Let r: She comes to work.

Which represents the statement "The day is Tuesday or Thursday if and only if she comes to work”?

p ↔ (q ∧ r)
p ↔ (q ∨ r)
(p ∧ q) ↔ r
(p ∨ q) ↔ r

Answer 1

The relation that denotes the condition:

"The day is Tuesday or Thursday if and only if she comes to work” is given by:

p∨q↔r

Hence, option D is true.

Explanation:

Let p: The day is Tuesday.

q: The day is Thursday.

r: She comes to work.

the day is Tuesday or Thursday is denoted by: p∨q

Hence the condition which represents that "The day is Tuesday or Thursday if and only if she comes to work”

is: p∨q↔r

Answer 2

It's definitely D: (p ∨ q) ↔ r