The question asks to identify the logical operator that evaluates to TRUE only when both conditions are TRUE. The options are OR, NOT, AND, and XOR.

Discrete MathematicsLogicBoolean AlgebraLogical OperatorsAND operator
2025/4/4

1. Problem Description

The question asks to identify the logical operator that evaluates to TRUE only when both conditions are TRUE. The options are OR, NOT, AND, and XOR.

2. Solution Steps

Let's analyze each logical operator:
- OR: The OR operator returns TRUE if at least one of the conditions is TRUE. It returns TRUE if both are true.
- NOT: The NOT operator returns the inverse of the condition. It returns TRUE if the condition is FALSE, and FALSE if the condition is TRUE. It operates on a single condition, not two.
- AND: The AND operator returns TRUE only when both conditions are TRUE. Otherwise, it returns FALSE.
- XOR: The XOR (exclusive OR) operator returns TRUE if the conditions are different (one is TRUE and the other is FALSE). It returns FALSE if both conditions are TRUE or both are FALSE.
Based on these definitions, the AND operator is the correct answer.

3. Final Answer

AND

Related problems in "Discrete Mathematics"

Question 11: Given sets $A = \{a, b, c\}$, $B = \{a, b, c, d, e\}$, and $C = \{a, b, c, d, e, f\}$, ...

Set TheoryUnionIntersectionModeMedianStatistics
2025/6/5

The given Venn diagram shows the number of elements that are multiples of 2 and multiples of 3. The ...

Venn DiagramsSet TheoryDivisibilityCounting
2025/6/4

The problem asks for the truth table for negation. Negation is a unary operation on a logical value,...

LogicTruth TablesNegation
2025/6/4

The problem is to complete the truth table for the logical expression $\neg P \wedge Q$. The table p...

Boolean AlgebraLogicTruth TablesPropositional Logic
2025/6/4

Given two sets $A = \{apple, banana, cherry\}$ and $B = \{red, yellow\}$, find the Cartesian product...

Set TheoryCartesian Product
2025/6/4

The problem asks us to draw a Venn diagram representing two sets, A and B. Set A contains the first ...

Set TheoryVenn DiagramsIntersection of SetsEven NumbersMultiples
2025/6/4

The problem asks when the logical implication $p \rightarrow q$ is considered true. We are given 5 o...

LogicTruth TablesImplication
2025/6/4

We are given that there are 4 boys and 5 girls standing in a line. We are asked to find: a) The tota...

PermutationsCombinationsCounting Principles
2025/6/4

The problem asks about the number of ways to arrange 4 math books, 3 physics books, and 2 chemistry ...

CombinatoricsPermutationsArrangementsFactorials
2025/6/4

We are given three sets $M$, $N$, and $\mu$. $M$ contains integers $x$ such that $2 \le x \le 6$, $N...

Set TheorySet OperationsComplementIntersection
2025/6/3