Question

A=(x:x is a prime number,x belongs to N andx<50) and B=(x:x=4p+1, p belongs to N, x<50).Then find A-B and A intersection B. [ANSWER WITH EXPLANATION] i follow you​

Answer 1

So, as A={ x:x is a prime number, x belongs to N and x<50}

Here, the x is a prime number and x should also be a natural number(counting number) and also x should be less than 50.

ans: A = { 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 }

and B = { x:x = 4p+1, p belongs to N and x <50 }

Here, x is equals to 4p+1 and p is a natural number and x should be less than 50.

now, replacing p with every natural number but the answer should be less than 50

4 × 1 +1 = 5

4×2+1 = 9

......( continuing it)

4×12+1 = 49

ans: B = { 5, 9, 13, 17, 21, 25, 29, 33, 37, 41 }

now, we found the elements of A and B, then answering the questions:

A-B

Here, we have to write the elements to A BUT we have to EXCLUDE all the elements of B. There should be no element of B.

ans: { 1, 2, 3, 5, 7, 11, 19, 23, 31, 37, 43, 47 }

A n B ( A intersection B)

Well here, we will write all COMMON elements of A and B.

ans: { 5, 13, 17, 29, 37, 41 }