Given A = {1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5}, check if (A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D) is true?

Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
A x (B U C) = (A x B) U (A x C)

Given the function f:x ⟶ x²- 5x + 6, evaluate
i) f( -1)
ii) f (2a)
iii) f (2)
iv) f (x - 1)

If the function f: R⟶ R defined by 
\(f(x)=\left\{\begin{array}{l} 2 x+7, x<-2 \\ x^{2}-2,-2 \leq x<3 \\ 3 x-2, x \geq 3 \end{array}\right.\)
(i) f( 4)
(ii) f( -2)
(iii) f(4) + 2f(1)
(iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}, Verify whether A x C is a subset of B x D?

If f(x) = \(\frac { x-1 }{ x+1 } \), x ≠ 1 show that f(f(x)) = -\(\frac{1}{x}\), provided x ≠ 0.

The functions f and g are defined by f(x) = 6x + 8; g(x) = \(\frac { x-2 }{ 3 } \)
i. Calculate the value of gg\(\left( \frac { 1 }{ 2 } \right) \)
ii. Write an expression for gf(x) in its simplest form.

Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
(A U B) x  C = (A x C) U (B x C)

Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that
A x ( B - C) = (A x B) - (A x C)

Find f o g and g and g o f when f(x) = 2x + 1 and g(x) = x² - 2