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(Not asking which one is right but they want numbers)Let S be a set with n eleme

ID: 3643110 • Letter: #

Question

(Not asking which one is right but they want numbers)Let S be a set with n elements and let a and b distinct elements of S. How many relations R are there on S such that :
a) (a,b) is an element of R?
b) (a,b) is not an element of R?
c) no ordered pair in R has a as its first element?
d) at least one ordered pair in R has a as its first element?
e)no ordered pair in R has a as its first element or b as its second element?
f) at least one ordered pair in R either has a as its first element of has b
as its second element?

Explanation / Answer

c) no ordered pair in R has a as its first element is correct