Which diagram represents the following sets?
2 answers:
Answer:
The answer is below
Step-by-step explanation:
An integer is a whole number which is either positive, negative or zero.
Given that:
P=(x | x is an integer divisible by 2}. An integer divisible by 2 can be represented by 2k, where k is an integer, hence:
P = (..., -6, -4, -2, 0, 2, 4, 6, ...)
Q= (x | x is an odd integer). An odd integer can be represented by 2k + 1, where k is an integer, hence:
Q = (..., -5, -3, -1, 1, 3, 5, 7, 9 ...)
R = (x | x is an integer divisible by 3). An integer divisible by 3 can be represented by 3k, where k is an integer, hence:
R = (..., -12, -9, -6, -3, 0, 3, 6, 9, ...)
From the above we can see that Q and P are disjoint set, that is P ∩ Q = 0
But P and R have common numbers (..., -6, 0, 6, 12,...) i.e. P ∩ R ≠ 0
Also Q and R have common numbers (..., -3, 3, 9,...) i.e. Q ∩ R ≠ 0
The question and answer is attached
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