Question

1. Given that U = {1, 2, 3, ..., 10}, S = {3, 5, 7, 9} and T = {4, 5, 6, 7}, find S-T​

Answer 1

The set of, S - T = {3, 9}

Define Set Operation.

To obtain a combination of components according to the operation done on them, the set operations are conducted on two or more sets.

In a set theory, there are three major types of operations performed on sets, such as:

1) Union of sets (∪)

2) Intersection of sets (∩)

3) Difference of sets ( – )

We know, S -T = S ∩ T'

Given, universal set is U = {1, 2, 3, ..., 10}

S = {3, 5, 7, 9} and T = {4, 5, 6, 7}

Now, find T' (T's compliment),

The complement of set T is defined as a set that contains the elements present in the universal set but not in set T.

T'  = {1, 2, 3, 8, 9, 10}

given, S = {3, 5, 7, 9}

Find, S ∩ T'

S ∩ T' = {3, 5, 7, 9} ∩ {1, 2, 3, 8, 9, 10}

The intersection of two sets S and T is a subset of the universal set U and contains elements that are present in both sets S and T. It is represented by the symbol "∩".

so, S ∩ T'  = {3, 9}

Hence, S - T = S ∩ T'  = {3, 9}

To read more about Set Operation.

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