Advertisements
Advertisements
Question
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∪ C).
Solution
A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}
B ∪ C = {4, 5, 6}
∴ A × (B ∪ C)
= {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}
APPEARS IN
RELATED QUESTIONS
Given an example of a relation. Which is Transitive but neither reflexive nor symmetric.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?
Give an example of a relation which is reflexive and symmetric but not transitive ?
Give an example of a relation which is symmetric and transitive but not reflexive?
Define a reflexive relation ?
Let R = {(a, a3) : a is a prime number less than 5} be a relation. Find the range of R.
The relation 'R' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .
Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .
If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is ____________ .
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∩ C).
The following defines a relation on N:
x is greater than y, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
The maximum number of equivalence relations on the set A = {1, 2, 3} are ______.
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is ____________.
The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is
If A is a finite set consisting of n elements, then the number of reflexive relations on A is
The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is
Read the following passage:
|
An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. |
Based on the above information, answer the following questions:
- How many relations are possible from B to G? (1)
- Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
- Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
OR
A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)
