❥︎If S and T are two sets such that S has 21 elements, T has 32 elements, and S∩T has 11 elements, how many elements does S∪T have?

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Step-by-step explanation:

We have to sets S and T. The number of elements in each set is given and the number of elements in the intersection of both sets is also given. Then we can find the number of elements in the union of both sets using the equation n(A∪B)=n(A)+n(B)−n(A∩B)Complete step by step solution:We are given to sets S and T.The number of elements of S is given as 21⇒n(S)=21The number of elements of T is given as 32⇒n(T)=32And number of elements of S∩T is 11⇒n(S∩T)=11We need to find the number of elements in S∪T or n(S∪T)We know that, n(S∪T)=n(S)+n(T)−n(S∩T)Substituting the values in the equation, we get,n(S∪T)=21+32−11On solving we get,⇒n(S∪T)=42Therefore, the number of elements in S ∪ T is 42.

The answer would be 5< 6n