Set Operations | MCQs

Explanation

If A = {1,2,3,4,6} B= {2,4,5,7} then B-A =?

{2,4,5,7} -  {1,2,3,4,6}

 B - A means B contains the element which is not present in A. 

{3,5,7}

Explanation

The expression {x|x ∈ A ∨ x ∈ B} represents the set of elements that are in A or in B or in both.

This is the definition of the union of two sets, denoted as A ∪ B.

Explanation

Given:

A = {2, 4, 6, 10}

The symbol ∈ means "is an element of".

Since 4 is an element of set A, the correct representation is:

4 ∈ A

Explanation

The shaded part in the Venn diagram represents Q - P, meaning elements that belong to set Q but not to P.

Explanation

Universal set (U) = {1, 2, 3, 4, 5, 6}

Set A = {2, 3}

Complement of A means all elements in U that are not in A → {1, 4, 5, 6}

Explanation

P(A) is the power set of A = {1, 2}, which includes all subsets: ∅, {1}, {2}, {1, 2}.

So, {2} is one of the subsets, hence it is an element of P(A).

Explanation

B - A represents the set of elements that are in B but not in A.

The correct notation is: {x | x ∈ B and x ∉ A}

Explanation

Using De Morgan's Law:

$$<b><font\; color="\#0000ff">(</font></b>\mathrm{<b><font\; color="\#0000ff">A</font></b>}<b><font\; color="\#0000ff">\cup </font></b>\mathrm{<b><font\; color="\#0000ff">B</font></b>}{<b><font\; color="\#0000ff">)</font></b>}^{\mathrm{<b><font\; color="\#0000ff">\prime </font></b>}}<b><font\; color="\#0000ff">=</font></b>{\mathrm{<b><font\; color="\#ff0000">A</font></b>}}^{\mathrm{<b><font\; color="\#ff0000">\prime </font></b>}}<b><font\; color="\#ff0000">\cap </font></b>{\mathrm{<b><font\; color="\#ff0000">B</font></b>}}^{\mathrm{\prime }}$$

Explanation

The given set is a set of sets, also known as a collection of sets. It contains two elements:

1. {1, 2, 3} (a set of three elements)
2. {4, 5} (a set of two elements)

Explanation

The distributive property of set operations states that:

A × (B ∪ C) = (A × B) ∪ (A × C)