If , show that.

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:

i. A x C B x D

ii. A x (B ∩ C) = (A x B) ∩ (A x C)

Let A be the set of first five natural and let R be a relation on A defined as follows: (x, y) R x ≤ y

Express R and R^-1 as sets of ordered pairs. Determine also

i. the domain of R^‑1

ii. The Range of R.

Find the domain of the function of real variable.

If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically:

i. A x B

ii. B x A

iii A x A iv. B x B