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# The sentence "____ if and only if $x + x = 3x$" is TRUE. Which of the following could be used to fill in the blank?

$\begin {array} {1 1} (A)\;x + x = 2x & \quad (B)\;2x - x = 2x \\ (C)\;both\: 1 \: and \: 2 \: could\: be\: used & \quad (D)\;neither\: 1\: nor\: 2\: could \: be\: used \end {array}$

Ans : (B)
"if and only if" is TRUE when both conditions are the SAME truth value.
Since $"x + x = 3x"$ is false, the first condition must also be false.
$2x - x = 2x$ is false.