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Question

State which of the following sets are disjoint
(i) A={2,4,6,8};B= { x:x is an even number <10,xN}
(ii) X={1,3,5,7,9},Y={0,2,4,6,8,10}
(iii) P= { x:x is a prime <15}
Q={ x:x is a multiple of 2 and x<16}
(iv) R={a,b,c,d,e},S={d,e,a,b,c}

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Solution

If two sets A and B are said to be disjoint ifAB=ϕ.
(1)A={2,4,6,8}
B={2,4,6,8}
A=B
So, A and B are not disjoint.
(2)X={1,3,5,7,9}
Y={0,2,4,6,8,10}
XY=ϕ
So, X and Y are disjoint.
(3)P={2,3,5,7,11,13}
Q={.........4,2,0,2,4,6,8,10,12,14}
PQ={2}
So, P and Q are not disjoint.
(4)R={a,b,c,d,e}
S={d,e,a,b,c}
RS={a,b,c,d,e}
So, R and S are not disjoint.

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