Question

A = {x:x is a factor of 56}
B = {x : x is a multiple of 4 and x < 30)
Find (A - B) U (A - B) and (A-B) n(An B).​

Answer 1

Answer:

(A-B) U (A-B) ={2,7}

(A-B) n(A-B) ={2,7}

Step-by-step explanation:

A={x:xis a factor of 56}

it means elements of A are factors of 56

now we do prime factorization of 56

56=7×2×2×2

but in set we can take one element once only

so

A={2,7}

B={x:xis a multiple of 4,x<30}

it means elements of B are multiple of 4 and less than 30

multiple of 4 which are less than 30 are

4,8,12,16,20,24,28

so

B={4,8,12,16,20,24,28}

now

(A-B) contain the elements which are in A but not in B

A-B={2,7} - {4,8,12,16,20,24,28}

here 2,7 are in A but not in B so

A-B ={2,7}

now

(A-B)U(A-B) ={2,7}U{2,7}

To find union of two sets we must take all elements of both sets

so (A-B) U (A-B) ={2,7}

now

(A-B) n(A-B) ={2,7}n{2,7}

To find intersection of two sets we must take common elements so

(A-B) n (A-B) ={2,7}

Hope it helps you

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