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

Question
Integrals
asked 2020-12-25
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

Answers (1)

2020-12-26
Given sets A,B,C 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}
Given sets A,B,C 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}
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
0

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