Intersection | MCQs

Explanation

Total students = 26

Students who like football = 21

Students who like cricket = 14

Let x be the number of students who like both football and cricket.

Using the formula:

(Football ∪ Cricket) = Football + Cricket – Both

So,

26 = 21 + 14 – x

26 = 35 – x

x = 35 – 26

x = 9

Explanation

The symbol ∩ represents the common elements between two or more sets.

For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.

Explanation

Step 1: Find A'

A' = I - A = {a, b, c, e, f, g} - {b, e, f} = {a, c, g}.

Step 2: Find B'

B' = I - B = {a, b, c, e, f, g} - {a, b, c} = {e, f, g}.

Step 3: Find A' ∩ B'

A' ∩ B' = {a, c, g} ∩ {e, f, g} = {g}.

Explanation

The union of two sets A and B (denoted as A ∪ B) includes all elements that are in A, in B, or in both.

It represents the total collection of elements from both sets without repetition.

Explanation

Given:

A ∪ B = A ∩ B

This equation implies that every element that is in A or B (or both) is also in both A and B.

This can only be true if:

A = B

or, in other words, A and B have exactly the same elements.

Explanation

Given the expression (A and x∈B) represents the condition where x belongs to both A and B:

This directly implies the intersection of sets A and B.

Explanation

If two circles touch externally, the distance between their centers is equal to the sum of their radii.

This is because the circles are externally tangent, meaning the distance from one center to the other is the total length of both radii combined.

Explanation

Skew lines are lines that are not parallel and do not intersect, and they exist in three-dimensional space.

They lie in different planes, unlike parallel or intersecting lines.

Explanation

To find the intersection of sets A and B, we need to identify the elements that are common to both sets

Set A contains the elements {1, 2, 3, 6}, and set B contains the elements {2, 4, 5, 7}.

The only element that appears in both sets is 2

Thus, the intersection A ∩ B is {2}

Explanation

Disjoint sets have no elements in common.

Therefore, their intersection is the null set (∅).