Set Equality Lets set A,B,C and D be defined as follows A={ninZ|n=2p, for some integers p} B={minZ|m=2q−1,for some integers q} c={kinZ|k=4r,for some integers r} is A=B IS A=C

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Set Equality  Lets set A,B,C and D be defined as follows  A={ninZ|n=2p, for some integers p}  B={minZ|m=2q−1,for some integers q}  c={kinZ|k=4r,for some integers r}  is A=B   IS A=C

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Given sets A,B,C be defined as follows  A={ninZ|n=2p, for some integers p}  B={minZ|m=2q−1,for some integers q}  C={kinZ|k=4r,for some integers r}  Given sets A,B,C be defined as follows  A={ninZ|n=2p, for some integers p}  B={minZ|m=2q−1,for some integers q}  c={kinZ|k=4r,for some integers r}  Steps:  Prove A=B  2p=2q-2  p=q-1  Given p and q are the integers.  If q is an integer, then (q-1) is also an integer.  Since, if take q = p-1 then A and B are equal.  Hence, A = B if q = p-1  Prove in the following that A = C.  n = 2p  and  k = 4r  Given, p and r are the integers.  Take p = 1 and r = 1, then  n = 2  and  k = 4  Therefore, for p = 1 and any value of r, A cannot be equal to C.  This shows that, A is not equal to C.  Hence, for any integer  AneC

Set Equality Lets set A,B,C and D be defined as follows A={ninZ|n=2p, for some integers p} B={m inZ|m=2q-1,for some integers q} c={kinZ|k=4r,for some integers r} is A=B IS A=C

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