Sets and Relation questions
385 published questions with worked solutions.
- Let Z be the set of integers. If A = x Z : 2^ (x+2)(x^2-5x+6) = 1 and B = x Z : -3 < 2x - 1 < 9 , then the number of subsets of...
- In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is...
- Let X= n N: 1 n 50 . If A= n X: n is a multiple of 2 and B= n X: n is a multiple of 7 , then the number of elements in the...
- If A= x R: |x|<2 and B= x R: |x-2| 3 ; then -
- Let R_1 and R_2 be two relations defined as follows : R_1= (a,b) R^2; a^2+b^2 Q and R_2= (a,b) R^2: a^2+b^2 Q , where Q is the...
- Consider the relations R_1 and R_2 defined as aR_1b ⇔ a² + b² = 1 for all a, b ∈ R and (a, b) R_2 (c, d) ⇔ a + d = b + c for all...
- Let A = 1, 2, 3, …, 20 . Let R_1 and R_2 two relation on A such that R_1 = (a, b) : b is divisible by a , R_2 = (a, b) : a is an...
- Let a relation R on N × N be defined as: (x_1, y_1) R (x_2, y_2) if and only if x_1 ≤ x_2 or y_1 ≤ y_2. Consider the two...
- In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied...
- Let the relations R₁ and R₂ on the set X = 1, 2, 3, ..., 20 be given by R₁ = (x, y) : 2x − 3y = 2 and R₂ = (x, y) : −5x + 4y = 0...
- Let A = 1, 2, 3, 4, 5 . Let R be a relation on A defined by xRy if and only if 4x ≤ 5y. Let m be the number of elements in R and...
- If R = (x, y) : x, y ∈ Z, x^2+3y^2 8 is a relation on the set of integers Z, then the domain of R^ -1 is:
- Let A = 2, 3, 6, 8, 9, 11 and B = 1, 4, 5, 10, 15 . Let R be a relation on A × B define by (a, b) R (c, d) if and only if 3ad −...
- A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% fo the people read both the...
- A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of...
- Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets...
- If A= x:f(x)=0 and B= x:g(x)=0 , then A B will be the set of roots of the equation
- Let A = 2, 3, 4, 5, 6 . Let R be a relation on the set A × A given by (x, y)R(z, w) if and only if x divides z and y ≤ w. Then...
- Let A= 1,4,7 and B= 2,3,8 . Then the number of elements, in the relation R= ((a₁,b₁),(a₂,b₂))∈((A×B)×(A×B)) : a₁+b₂ divides a₂+b₁...
- Let R= (x,y)∈ℕ×ℕ : log_e(x+y)≤2 . Then the minimum number of elements, required to be added in R to make it a transitive...
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