🔀 Logic

Boolean Algebra

Every if statement, SQL WHERE clause and search query relies on Boolean logic. Master evaluating expressions and reading truth tables here.

The building blocks

Operator	True when…
NOT A	A is FALSE
A AND B	Both A and B are TRUE
A OR B	At least one of A or B is TRUE

Order of operations (without brackets): NOT first, then AND, then OR — but always use brackets in exam answers to make your intended order explicit.

Evaluate step by step

Work outward from the innermost brackets, one operator at a time — never try to evaluate a whole expression in one leap.

(A AND B) OR C     where A=TRUE, B=TRUE, C=FALSE

Step 1: (A AND B) → (TRUE AND TRUE) → TRUE
Step 2: TRUE OR C → TRUE OR FALSE   → TRUE

Interactive truth table generator

Pick an expression below to see every possible combination of its variables and the resulting output — this is exactly how you'd build a truth table by hand in the exam.

Pick an expression to generate its full truth table:

A	B	A AND B
F	F	F
F	T	F
T	F	F
T	T	T

Test yourself

0/17 answered

Question 1

Given A = TRUE, B = FALSE, what is the result of (A AND B)?

Question 2

Given A = TRUE, B = FALSE, what is the result of (A OR B)?

Question 3

What is NOT(TRUE)?

Question 4

Evaluate (A AND B) OR C, given A = TRUE, B = TRUE, C = FALSE.

(A AND B) OR C

Question 5

Evaluate (A AND B) OR C, given A = FALSE, B = TRUE, C = FALSE.

(A AND B) OR C

Question 6

A learner qualifies for an award if: age is 16 or older, AND (has an A average OR is a prefect). age = 17, average = 'B', isPrefect = TRUE. Does the learner qualify?

age >= 16 AND (average == 'A' OR isPrefect)

Question 7

Which relational operator would you use in code to check that a value is 'not equal to' another in Java?

Question 8

In a search engine, which Boolean search would return results containing 'python' but excluding results about the reptile?

Question 9

Complete this row of a truth table for the expression (A OR B) AND NOT C, given A = FALSE, B = FALSE, C = FALSE.

(A OR B) AND NOT C

Question 10

What determines the order in which a Boolean expression without brackets is evaluated?

Question 11

How many rows does a complete truth table need for a Boolean expression with 3 distinct variables?

Question 12

Evaluate NOT(A AND B), given A = TRUE, B = TRUE.

NOT(A AND B)

Question 13

A discount applies if: totalSpend >= 500 OR isMember is TRUE, AND it is NOT a public holiday. totalSpend = 300, isMember = TRUE, isPublicHoliday = FALSE. Does the discount apply?

(totalSpend >= 500 OR isMember) AND NOT isPublicHoliday

Question 14

Evaluate A OR (B AND C), given A = FALSE, B = TRUE, C = FALSE.

A OR (B AND C)

Question 15

Which Java operator checks that BOTH of two boolean conditions are true, short-circuiting (skipping the second check) if the first is already false?

Question 16

A login is allowed if: username matches AND (password matches OR hasValidToken). username matches = TRUE, password matches = FALSE, hasValidToken = TRUE. Is login allowed?

usernameMatches AND (passwordMatches OR hasValidToken)

Question 17

According to De Morgan's Law, NOT(A AND B) is logically equivalent to which expression?