1) (x, y) ∈ S ⇔ x ≥ y 2) (x, y) ∈ S ⇔ x = y 3) (x, y) ∈ S ⇔ x - y is a multiple of 3 4) (x, y) ∈ S if |x - y| is even Solution: (1) (x, y)... View Article
Solution: (2) Reflexive: (m, m) ∈ R, (n, n) ∈ R Symmetric: (2, 6) ∈ R, (m, n) ∈ R, but (6, 2) ∉ R It is not symmetric. Transitive: (m, n)... View Article
1) aR1b ⇔ |a| = |b| 2) aR2b ⇔ a ≥ b 3) aR3b ⇔ a divides b 4) aR4b ⇔ a < b Solution: (1) (i) |a| = | b| Reflexive: (a, a) ∈ R a = a... View Article
Solution: (4) R is Reflexive (a, b) R (c, d) and (c, d) R (e, f) a + d = b + c c + f = d + e On adding, a + d + c + f = b + c + d + e ⇒... View Article
Solution: (3) R is reflexive when (a, a), (b, b), (c, c) ∈ R If (b, a) , (c, b) ∈ R, then R is symmetric. If (c, a), (a, c) ∈ R then R is... View Article
Solution: (2) The given relation is R = {(x, y) ∈ W × W : the words x and y have at least one letter in common} Reflexive: (a, a) ∈ R If a... View Article
Solution: A = {2, 4, 6} B = {2, 3 ,5} If set A has m elements and set B has n elements, then the number of relations = 2mn Here m = 3, n... View Article
Let R be the real line consider the following subsets of the plane R × R ,S = {(x, y) / y = x + 1 and 0 < x < 2}, T = {(x, y) / x - y is an... View Article
1) R = {(0,3), (0,-3), (3,0), (-3,0)} 2) Domain of R = {-3,0,3} 3) Range of R = {-3,0,3} 4) None of the above Solution: (4) x2 + y2 = 9 x... View Article
The relation ≤ on numbers has the following properties. (i) a ≤ a ∀ a ϵ R (Reflexivity) (ii) If a ≤ b and b ≤ a then a = b ∀ a, b ϵ R... View Article
Solution: (1) A set has n elements and the relation is said to be reflexive if it consists of at least n ordered pairs. There exists m ordered... View Article
If A = {x ∈ R / f (x) = 0} and B = {x ∈ R / g (x) = 0} then A ⋂ B = 1) ϕ 2) {x ∈ R / f (x) = 0} 3) {x ∈ R / f (x) + g (x) = 0} 4) {x ∈ R / f... View Article
If the delta G is positive, the reaction is said to be favoured as the reverse reaction. Stay tuned with BYJU’S to learn more about other... View Article