Show that if A ⊂ B, then C – B ⊂ C – A

Solution:

In mathematics, a set is a well-defined collection of objects. Sets are named and represented using a capital letter.

In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc

The difference between two sets A and B is denoted by A - B and it contains all elements that are in set A which are NOT in set B.

Let A ⊂ B and x ∈ (C – B)

⇒ x ∈ C and x ∉ B ... (1)

⇒ x ∉ A [Since A ⊂ B]

⇒ x ∈ C and x ∉ A (from (1)

⇒ x ∈ (C – A)

Therefore,

C – B ⊂ C – A

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 5

Show that if A ⊂ B, then C – B ⊂ C – A

Summary:

If A ⊂ B, then we have shown that C – B ⊂ C – A