Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C

Solution:

It is given that A, B and C be the sets such that A υ B = A υ C and A ∩ B = A ∩ C.

Let x ∈ B

Therefore,

x ∈ A υ B

Since, A υ B = A υ C ; x ∈ A υ C

Hence, x ∈ A or x ∈ C

If x ∈ A

Then x ∈ A ∩ B

Since A ∩ B = A ∩ C, x ∈ A ∩ C

That means, x ∈ A and x ∈ C

So, B ⊂ C

Similarly,

we can show that C ⊂ B.

Hence, B = C proved

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NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 3

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.

Solution:

If A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, we have shown that B = C