Question

Which of the following biconditional statements are true?

• A. $2\ne 3\leftrightarrow 2>3\mathrm{or}2<3$
• B. $2=3\leftrightarrow 3=4$
• C. $a<3\leftrightarrow a>3$
• D. $a=3\leftrightarrow a\le 3\mathrm{and}a\ge 3$

Answer 1

Answer: (A), (B), (D)

$a=3\leftrightarrow a\le 3\mathrm{and}a\ge 3$

A biconditional statement is true either if both the statements are true or if both the statements are false.
a. $2\ne 3\leftrightarrow 2>3\mathrm{or}2<3$
Both these statements are true .
b. $2=3\leftrightarrow 3=4$
Both these statements are false .
c. $a<3\leftrightarrow a>3$
If one statement is true the other is false.
d. $a=3\leftrightarrow a\le 3\mathrm{and}a\ge 3$
If one is true the other is also true .