Question

If X = {1, 2, 3, .. 10} and A = {1, 2, 3, 4, 5}, find the number of sets B ⊆X such that

A - B = {4}​

Answer 1

Step-by-step explanation:

Given, X={1,2,3,....,10}

and A={1,2,3,4,5}

Now, A−B={4}

⇒B=A−{4}={1,2,3,4,5}−{4}

={1,2,3,5}

∴X−{4}−B

={1,2,3,...,10}−{4}−{1,2,3,5}

={6,7,8,9,10}

Therefore,number of subsets B of X i.e., {6,7,8,9,10} = 2raise to the power 5