Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A :Cߏ∩B ≠ φ} is _____________.
Correct Answer: 112
Solution and Explanation
The correct answer is 112
As Cߏ∩B≠φ, c must be not be formed by {1, 2, 4, 5}
∴ Number of subsets of A = 27 = 128
and number of subsets formed by {1, 2, 4, 5} = 16
∴ Required no. of subsets = 27 – 24 = 128 – 16
= 112
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Concepts Used:
Sets
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
Read More: Set Theory
Elements of a Set:
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
Read Also: Set Operation
Cardinal Number of a Set:
The cardinal number, cardinality, or order of a set indicates the total number of elements in the set.
Read More: Types of Sets