1. The problem asks to identify which proposition has truth value True (T). 2. Let's analyze each option: - A. $(\exists x \in \mathbb{R})(\forall y \in \mathbb{R})(x - 2y = y - x)$ means there exists a real number $x$ such that for all real $y$, $x - 2y = y - x$. Simplify: $$x - 2y = y - x \implies x + x = y + 2y \implies 2x = 3y$$ For this to hold for all $y$, $2x = 3y$ must be true for all $y$, which is impossible since $x$ is fixed and $y$ varies. So this is False. - B. "Whenever $\sqrt{3}$ is rational, $\sqrt{9}$ is rational." Since $\sqrt{3}$ is irrational, the antecedent is false, so the implication is true (an implication with false antecedent is true). So this is True. - C. $(\forall x \in \mathbb{Z})(\exists y \in \mathbb{Z})(x^2 + y^2 = 9)$ means for every integer $x$, there exists an integer $y$ such that $x^2 + y^2 = 9$. For example, if $x=3$, then $y^2=0$ so $y=0$ works. If $x=2$, $y^2=5$ which is not a perfect square, so no integer $y$ exists. So this is False. - D. "May God bless you" is not a proposition (no truth value). 3. Therefore, the proposition with truth value True is option B. Final answer: B