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Question

Let S be a set of all distinct numbers of the form PQ , where p,q1,2,3,4,5,6. What is the cardinality of the set S?


A

21

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B

23

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C

32

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D

36

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Solution

The correct option is B

23


Explanation For The Correct Option:

Finding is the cardinality of the set S

The number of elements taken at a time =2

So, the total possible numbers of form pq​ when pqis =26C2=30

Possible numbers when p=q is =6C1=6

Therefore the total numbers is =30+6=36

11=22=33=44=55=66

So subtracting 5 from the cardinality of the set.

12=24=36 [subtract 2 from the cardinality of the set]

21=42=63 [subtracting 2 from the cardinality of the set]

13=26 [subtracting 1 from the cardinality of the set]

31=62 [subtracting 1 from the cardinality of the set]

23=46 [subtracting 1 from the cardinality of the set]

32=64 [subtracting 1 from the cardinality of the set]

So, the cardinality of set =365221111=23.

Hence, the correct option is (B)


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