Practice Conditional Statement in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A conditional Pโ†’QP \to Q is a statement meaning "if PP is true, then QQ must be true," read as "if PP then QQ."

A promise or rule: if the condition holds, the consequence follows.

Showing a random 20 of 50 problems.

Example 1

medium
Rewrite 'no odd number is divisible by 2' as a conditional.

Example 2

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

Example 3

hard
Pโ†’QP \to Q is true and Qโ†’RQ \to R is true. By hypothetical syllogism, what conditional follows?

Example 4

hard
Determine the truth value: 'If 2\sqrt{2} is rational, then ฯ€\pi is rational.'

Example 5

easy
For Pโ†’QP \to Q with PP false and QQ true, what is its truth value?

Example 6

medium
Express 'being divisible by 44 is sufficient for being even' as a conditional.

Example 7

medium
If 'Pโ†’QP \to Q' is true and PP is true, what can you conclude about QQ?

Example 8

challenge
Find a quadrilateral that is a counterexample to the converse of: 'If a quadrilateral is a rhombus, then its diagonals are perpendicular.'

Example 9

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

Example 10

medium
Express 'a positive number is necessary for the log to be defined' as a conditional.

Example 11

challenge
Prove that Pโ†’QP \to Q is logically equivalent to ยฌPโˆจQ\neg P \lor Q using truth values.

Example 12

easy
For Pโ†’QP \to Q with PP false and QQ false, what is its truth value?

Example 13

easy
For Pโ†’QP \to Q with PP true and QQ false, what is its truth value?

Example 14

easy
Rewrite 'every multiple of 4 is even' as an if-then conditional.

Example 15

challenge
Prove using a truth table that Pโ†’QP \to Q and ยฌQโ†’ยฌP\neg Q \to \neg P are logically equivalent.

Example 16

medium
For statements P,QP, Q, in how many of the four truth-value rows is Pโ†’QP \to Q true?

Example 17

medium
Give a counterexample showing the converse of 'if nn is a multiple of 4, then nn is even' is false.

Example 18

easy
Write the inverse of Pโ†’QP \to Q.

Example 19

medium
How many rows of a 22-variable truth table make Pโ†’QP \to Q false?

Example 20

hard
Affirming the consequent is invalid. Given Pโ†’QP \to Q true and QQ true, can we conclude PP? Answer 11 for yes, 00 for no.
โ† Back to Conditional Statement Worked Examples Formula Explained