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Let A=\2, 3, 4, 5, 6\. Let R be a relation on the set A A given by (x, y)R(z, w) if and only if x divides z and y w. Then the number of elements in R is .
120
An element of R is ((x, y), (z, w)) with x z and y w; the two conditions are independent.
Pairs (x, z) with x z, x, z A:
x=2: z=2, 4, 6 (3); x=3: z=3, 6 (2); x=4, 5, 6: z=x (1 each)
3+2+1+1+1=8
Pairs (y, w) with y w: 5+4+3+2+1=15
n(R)=8 15=120
Answer: 120
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