Practice And Statements (Conjunction) 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 conjunction $P \wedge Q$ is a compound statement that is true if and only if both constituent statements $P$ and $Q$ are individually true.

To enter a theme park ride, you must be tall enough AND have a valid ticket—both conditions must hold. If you are tall enough but lost your ticket, you cannot ride. A conjunction $P \wedge Q$ works the same way: it is true only when every single part is true, and false the moment any part fails.

Showing a random 20 of 50 problems.

Example 1

easy

Evaluate: '

3>2

AND

5>4

Example 2

medium

Translate to logic and evaluate: '

\sqrt{16}=4

and

0

is positive'.

Example 3

medium

Show

P \wedge P \equiv P

(idempotence).

Example 4

challenge

Find all integers

n

with

1 \le n \le 100

satisfying '

n

is divisible by

3

AND

n

is divisible by

5

Example 5

easy

If both

P

and

Q

are false, what is

P \wedge Q

Example 6

easy

How many rows of the truth table for

P \wedge Q

are TRUE?

Example 7

medium

For '

x^2=4

AND

x>0

', find all real

x

Example 8

challenge

Show '

P \wedge (Q \vee R)

' equals '

(P\wedge Q)\vee(P\wedge R)

' (distributivity).

Example 9

easy

Let

p

: '

4

is even' and

q

: '

4 < 10

'. Evaluate

p \land q

p \land \neg q

, and

\neg p \land q

Example 10

easy

What is the symbol for logical AND?

Example 11

medium

For what

x

is '

x>0

AND

x<5

' true? Express as an interval.

Example 12

medium

Determine the truth value of: '

\sqrt{2}

is irrational AND

2+2=4

Example 13

medium

Construct the full truth table for

p \land q

and use it to show that conjunction is commutative:

p \land q \equiv q \land p

Example 14

easy

Translate to symbols: 'It is raining AND it is cold.' Let

R

= raining,

C

= cold.

Example 15

medium

Evaluate '

P \wedge Q

' where

P

: '

10

is divisible by

5

' and

Q

: '

10

is divisible by

4

Example 16

easy

In everyday speech 'tall enough AND has a ticket', can you ride with only a ticket?

Example 17

easy

How many of the 4 truth-table rows make

P\wedge Q

true?

Example 18

easy

Evaluate: '

4

is even AND

4

is prime'.

Example 19

easy

In set theory, which operation matches logical AND on predicates?

Example 20

easy

Determine the truth value of: (a) '

3 > 2

and

3 < 5

', (b) '

3 > 2

and

3 > 5

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Related Concepts

Logical Statement Or Statements (Disjunction)Truth Table