Practice Logical Operators in CS Thinking

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

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Quick Recap

Operators that combine or modify boolean expressions: AND (true only when both operands are true), OR (true when at least one operand is true), and NOT (reverses a boolean value from true to false or vice versa).

AND is strict (both must be true), OR is flexible (either works), NOT flips the result.

Showing a random 20 of 50 problems.

Example 1

medium
Evaluate NOT (True OR False) AND True\text{NOT (True OR False) AND True} using precedence.

Example 2

easy
Evaluate: True AND True AND False\text{True AND True AND False}.

Example 3

medium
Access is granted if `(isAdmin OR isOwner) AND NOT isBanned`. For isAdmin=False, isOwner=True, isBanned=False, is access granted?

Example 4

hard
Show that A XOR B≡(A AND NOT B) OR (NOT A AND B)A \text{ XOR } B \equiv (A \text{ AND NOT } B) \text{ OR }(\text{NOT } A \text{ AND } B) by testing (A,B)=(T,F)(A,B) = (\text{T},\text{F}).

Example 5

medium
Evaluate (A AND B) OR (A AND NOT B)(A \text{ AND } B) \text{ OR } (A \text{ AND NOT } B) for A=A=True, B=B=False.

Example 6

challenge
XOR can be built from AND, OR, NOT. Verify that A XOR B=(A OR B) AND NOT(A AND B)A \text{ XOR } B = (A \text{ OR } B) \text{ AND NOT}(A \text{ AND } B) for A=True,B=TrueA=\text{True}, B=\text{True}.

Example 7

challenge
Write the negation of 'every student passed' using logical operators (formally).

Example 8

medium
How many rows are in the truth table for an expression with 5 boolean variables?

Example 9

hard
Simplify: (A AND B) OR (A AND NOT B)(A \text{ AND } B) \text{ OR }(A \text{ AND NOT } B).

Example 10

medium
Using De Morgan's law, rewrite NOT (A OR B)\text{NOT (A OR B)} without the outer NOT.

Example 11

medium
Evaluate A AND NOT B OR CA \text{ AND NOT } B \text{ OR } C for A=A=True, B=B=True, C=C=False, using standard precedence.

Example 12

medium
If short-circuit AND is used and `A AND B` evaluates only A when A is False, what design rule does this enable?

Example 13

easy
How many rows does the truth table for AA AND BB have?

Example 14

hard
Why is `{NAND}` (NOT AND) considered functionally complete on its own?

Example 15

hard
Three variables A,B,CA, B, C. Build a truth-table expression that is True only when EXACTLY one of them is true.

Example 16

medium
Identify the bug: `if (x = 0 OR 1 OR 2)` is meant to test whether x is 0, 1, or 2.

Example 17

medium
A short-circuit AND `A AND B` skips evaluating B when A is false. If A is `False`, is B evaluated?

Example 18

medium
For a discount, a customer needs (age over 65) OR (student AND member). If age=70, student=False, member=False, does the customer qualify?

Example 19

easy
Evaluate: NOT False\text{NOT False}.

Example 20

easy
Evaluate: NOT True\text{NOT True}.
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