Use implication, converse, equivalence, negation, contrapositive.

Consider the proposition $p \rightarrow q$ where $p$ is "$x^2 = 16$" and $q$ is "$x = 4$". a) State the converse of this proposition. (1 mark) b) Determine whether the original proposition $p \rightarrow q$ is true or false. Justify your answer. (1 mark) c) Use your result from part b) to show that the original proposition and its converse are not equivalent. (1 mark)

Let $p$ be the statement "$x$ is divisible by 6" and $q$ be the statement "$x$ is divisible by 3", where $x \in \mathbb{Z}^+$. What is the contrapositive of the implication $p \Rightarrow q$?

Let p be the statement "x is divisible by 6" and q be the statement "x is divisible by 3", where x ∈ ℤ⁺. Which of the following is the contrapositive of the implication p ⇒ q?

Consider the conditional statement shown in the Venn diagram below. Determine which of the following statements is the contrapositive of the conditional statement represented.