Conditional Statement Math Example 2

Follow the full solution, then compare it with the other examples linked below.

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Determine the truth value of: 'If

2 > 5

, then

10 > 3

1
Identify the hypothesis $p$ : ' $2 > 5$ ' which is false.
2
A conditional $p \Rightarrow q$ is false only when $p$ is true and $q$ is false.
3
Since $p$ is false, the conditional is true regardless of $q$ . This is called vacuous truth.

Answer

\text{True (vacuously)}

A conditional statement with a false hypothesis is always true. This is a key principle in logic that often surprises students.

About Conditional Statement

A conditional $P \to Q$ is a statement meaning "if $P$ is true, then $Q$ must be true," read as "if $P$ then $Q$ ."

Write the converse, inverse, and contrapositive of: 'If a number is divisible by 6, then it is divis

Identify the hypothesis and conclusion in: 'If it rains, then the ground is wet.'

Identify the hypothesis and the conclusion in the statement: 'If a number is divisible by 4, then it