how many relations can AXB hare, if set A
has four elements & Set B has 3 elements?
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1
Answer:
A relation on AxB is, by definition, a subset of AxB. (If A and B are the same, then a relation on AxA is also called a relation on A.). If A has four elements and B has three elements, then AxB has 4*3=12 elements. So the question becomes, How many subsets are there of a 12-element set?
The number of subsets of an n element set is 2^n, so the number of relations on AxB is 2^12=4096. It’s hard to imagine that there are so many relations on two sets that are so small! To help understand this, write out all 2^4=16 relations if A consists of a and c and B consists of b and d.
Hope it helps.
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0
Answer:
answer is 2^⁴*³ as any relation has its subset 2^pq where p and q are no. of elements in two sets
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