1. **Problem:** Determine which one of the following is a proposition whose truth value is True (T). Given options: A. $(\exists x \in \mathbb{R})(\forall y \in \mathbb{R})(x - 2y = y - x)$ B. Whenever $\sqrt{3}$ is rational, $\sqrt{9}$ is rational. C. $(\forall x \in \mathbb{Z})(\exists y \in \mathbb{Z})(x^2 + y^2 = 9)$ D. May God bless you (not a proposition). 2. **Formula and rules:** - A proposition is a statement that is either true or false. - Quantifiers $\exists$ means "there exists" and $\forall$ means "for all". - Truth value T means the statement is true. 3. **Step-by-step analysis:** - Option A: Check if there exists an $x$ such that for all $y$, $x - 2y = y - x$. Simplify: $x - 2y = y - x \implies x + x = y + 2y \implies 2x = 3y$ for all $y$. This means $2x$ must equal $3y$ for every real $y$, which is impossible since $x$ is fixed and $y$ varies. So, A is false. - Option 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, B is true. - Option C: For all integers $x$, there exists an integer $y$ such that $x^2 + y^2 = 9$. For example, if $x=4$, $4^2=16$, then $y^2=9-16=-7$, no integer $y$ satisfies this. So, C is false. - Option D: "May God bless you" is not a proposition (no truth value). 4. **Conclusion:** The only true proposition is option B. **Final answer:** B