Question

Let p: The integer has one digit.

Let q: The integer is less than 10.
Which represents "The integer has one digit if and only if the integer is less than 10”?

p ∨ q
p ∧ q
p → q
p ↔ q

Answer 1

p ↔ q

Explanation:

Given :

Let p: The integer has one digit.

Let q: The integer is less than 10.

To Find:Which represents "The integer has one digit if and only if the integer is less than 10”?

Solution:

1. p ∧ q denotes “p and q”

2.p ∨ q denotes “p or q" (or both)

3.p → q denotes “if p then q”

4. Biconditional p ↔ q denotes “p if and only if q"

Thus Biconditional p ↔ q represents "The integer has one digit if and only if the integer is less than 10”

Hence Option D is correct p ↔ q