Explanation

Calculating the Number of Relations

Number of elements in A = 2

Number of elements in B = 3

Number of elements in A × B = 2 × 3 = 6

Calculating the Number of Relations

Number of relations = 2^6 = 64

Explanation

Understanding the Symmetric Difference

AΔB = (A ∪ B) - (A ∩ B)

Given: A ∪ B = {a, c, e, i, m, n, o} and A ∩ B = {e, i, o}

Calculating the Symmetric Difference

AΔB = {a, c, e, i, m, n, o} - {e, i, o}

= {a, c, m, n}

Explanation

Finding the Conjugate of z bar

Given: z = 3 + 4i

The conjugate of z, denoted as z bar, is 3 - 4i.

The conjugate of z bar is 3 + 4i.

Explanation

√68 = √4×17 = 2√17

Explanation

Suleman’s youngest son is the most intelligent of all.

This correctly uses the superlative degree (most intelligent) for comparing within a group.

Explanation

The leaves had turned brown.

Past Perfect tense uses had + past participle to show an action completed before another past action or time.

Here, had turned is in Past Perfect tense.

Explanation

"Read" here refers to an action completed in the past without any connection to the present.

Past simple tense uses the past form of the verb (read → pronounced red in past tense).

Explanation

I am very glad to be here.

A declarative sentence makes a simple statement and ends with a period.

Explanation

Unhappy describes Akhtar’s state, completing the meaning of the verb, so it’s a subject complement.

It is not an object because it doesn’t receive the action; it just tells more about the subject.

Explanation

We use care for to mean looking after or showing concern.

Correct sentence: The king Bruce cared for his people.