Practice Truth Table in Math

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

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Quick Recap

A table that systematically lists every possible combination of truth values for the input variables and the resulting truth value of the expression.

List every possible combination of T/F for inputs, and compute the output.

Showing a random 20 of 50 problems.

Example 1

challenge
Show, using a truth table, that P→QP \to Q and its converse Q→PQ \to P are NOT logically equivalent.

Example 2

medium
In the truth table for P∧¬QP \land \neg Q, which single row makes it true?

Example 3

medium
Use a truth table to determine whether ¬(p∨q)\neg(p \lor q) and ¬p∧¬q\neg p \land \neg q are equivalent.

Example 4

challenge
Use a truth table to prove De Morgan's law ¬(P∧Q)≡¬P∨¬Q\neg(P \land Q) \equiv \neg P \lor \neg Q.

Example 5

easy
How many rows does a truth table for 3 variables have?

Example 6

easy
In the row P=F,Q=TP = F, Q = T, what is the value of P→QP \to Q?

Example 7

easy
How many rows does a truth table for 2 variables P,QP, Q have?

Example 8

easy
In the row P=T,Q=TP = T, Q = T, what is the value of P∧QP \land Q (AND)?

Example 9

easy
How many rows does a truth table for n=5n = 5 variables have?

Example 10

easy
In the row p=T,q=Tp = T, q = T, what is the value of p↔qp \leftrightarrow q (biconditional)?

Example 11

hard
In the truth table for (p→q)∧(¬p→q)(p \to q) \land (\neg p \to q) in 2 variables, in how many of the 4 rows is the expression true?

Example 12

medium
Construct the truth table for p∧¬qp \land \neg q.

Example 13

medium
In the truth table for p∧(q∨r)p \land (q \lor r) with 3 variables, in how many of the 8 rows is it true?

Example 14

easy
In the row P=TP = T, what is the value of ¬P\neg P (NOT)?

Example 15

hard
Use a truth table to determine whether p→(q→r)p \to (q \to r) is equivalent to (p∧q)→r(p \land q) \to r.

Example 16

medium
Is p→(p∨q)p \to (p \lor q) a tautology?

Example 17

medium
In a truth table for P⊕QP \oplus Q (exclusive or), which rows are true?

Example 18

medium
Determine whether (p→q)∨(q→p)(p \to q) \lor (q \to p) is a tautology.

Example 19

medium
Construct the truth table for ¬P∨Q\neg P \lor Q and compare it to P→QP \to Q.

Example 20

easy
Construct the truth table for p⇒qp \Rightarrow q.
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Related Concepts

Logical Statement