Question

Which three biconditional statements are true?

a) "The number 117 is divisible by 9 if and only if the sum of the digits in 117 is evenly divisible by 9."
b) "A pentagon has five sides if and only if each angle measure is equal."
c) "10 + 10 = 20 if and only if 2 × 10 = 20."
d) "A rhombus is a square if and only if its opposite angles are equal."
e) "A number is divisible by 3 if and only if it’s divisible by 6."
f) "The number 7 is even if and only if it’s divisible by 2."

Answer 1

The three biconditional statements that are true are: 1) The number 117 is divisible by 9 if and only if the sum of the digits in 117 is evenly divisible by 9. 2) 10 + 10 = 20 if and only if 2 × 10 = 20. 3) A rhombus is a square if and only if its opposite angles are equal.

Step-by-step explanation:

The three biconditional statements that are true are:

a) "The number 117 is divisible by 9 if and only if the sum of the digits in 117 is evenly divisible by 9."

c) "10 + 10 = 20 if and only if 2 × 10 = 20."

d) "A rhombus is a square if and only if its opposite angles are equal."

These statements hold true because they express a two-way logical relationship. In each statement, both conditions must be true for the biconditional statement to be true.