Let A and B be sets. Show that
`f: AxxB to BxxA` such that
`f(a,b) = (b,a)` is a bijective function

Let A be a non - empty set such that A xx B=A xx C show that B=C

Show that the function f:RrarrR given by f(x)=x+x^3 is a bijective function.

If f: R rarr R be a function defined by f(x)=4 x^3-7 , show that the function f is a bijective function.

Let A,B and C be the sets such that A cup B = A cup C and A cap B = A cap C . Show that B = C.

Let f, g, and h be functions from R to R. Show that (f + g) o h = foh + goh

A die is thrown at random Let A and B be the evnts that the "die shows an even number " the die shows a prime number" respectively. Write down A nd B sets

Let A be the set of all students of a boys school. Show that the relation R in A given by R ={(a, b): a is sister of b} is the empty relation and R' ={(a, b): the difference between heights of a and b is less than 3 meters} is the universal relation.

Let f: N rarr N where N is set of natural numbers be a function such that f(x + y)=f(xy) AA x ge4 and y ge4 , then a)f(4) = f(5) b)f(8) = f(9) c)f(7) = f(8) d)f(5) = f(6)

Let f be the subset of Z xx Z defined by f = {(ab, a + b) : a,b in Z} is f a function from Z to Z? justify your answer.