CUET Mathematics 2022 16 July Shift 2 PYQs

Which of the following are correct?

(A) If a ≡ b(mod n), then -a ≡ -b (mod n)

(B) If a + b = c, then a(mod n) + b(mod n) ≡ (a + b + c)(mod n).

(C) If a ≡ b (mod n), then ka ≡ kb(mod n), ∀ k ∈ I.

(D) If a ≡ b (mod n), then (a + k) ≡ (b + k)(mod n), ∀ k ∈ I.

Choose the correct answer from the options given below:

Which of the following relations on the set $A = \{1, 2, 3\}$ are equivalence ?

(A) $R = \{(1,1), (2,2), (1,2), (2,1)\}$

(B) $R = \{(1,1), (2,2), (3,3)\}$

(C) $R = \{(1,1), (1,2), (2,1)\}$

(D) $R = \{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2), (1,3), (3,1)\}$

(E) $R = \{(1,1), (2,2), (3,3), (1,2)\}$

Choose the correct answer from the options given below :

Given relation $R = \{(x, y) : y = x + 5, x < 4, x, y \in N\}$. Where N is a set of natural numbers then :