Question

out of 40 children, 30 can swim, 27 can play chess and 5 can do neither. How many children can swim only​

Answer 1

The Number of children who can swim only is 8.

Step-by-step explanation:

We are given that out of 40 children, 30 can swim, 27 can play chess and 5 can do neither.

This means n(T) = 40 which represents total children.

So, number of children who can swim = n(S) = 30

Number of children who can play chess = n(C) = 27

Number of children who neither swim nor ply chess = n(S' $\bigcap$ C') = 5

This means, the number of children who can swim or can play chess = n(S $\bigcup$ C) = n(T) - n(S' $\bigcap$ C') = 40 - 5 = 35

As we know that;

    n(S $\bigcup$ C)  =  n(S) + n(C) - n(S $\bigcap$ C)

Here, n(S $\bigcap$ C)  represents number of children who scan swim and can also play chess.

So,    n(S $\bigcup$ C)  =  n(S) + n(C) - n(S $\bigcap$ C)

         n(S $\bigcap$ C)  =  n(S) + n(C) - n(S $\bigcup$ C)

                         =  30 + 27 - 35

         n(S $\bigcap$ C)  =  57 - 35 = 22

Now, the number of children who can swim only = n(S) - n(S $\bigcap$ C)

                                                                                 = 30 - 22 = 8 children.

Hence, 8 children can swim only​.

Answer 2

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