Some group (G, o) is known to be abelian. Then, which one of the following is true for G?
Since group is abelian so it is commutative as well as associative.
Let R be a sym m etric and transitive relation on a set A Then
A relation which is symmetric and transitive, need not foe reflexive relation.
(i) R = {}; on the set A = {a, b}. The relation R is symmetric and transitive but not reflexive.
(ii) R = {(a, a), (b, b)}; on the set A = {a, b}.
The relation R is symmetric, transitive and also reflexive.
∴ A relation is transitive and symmetric relation but need not be reflexive relation.
Let A and B be sets and let A^{c} and B^{c} denote the complements of the sets A and B. The set (A  B) ∪ (B  A) ∪ (A ∩ B) is equal to
Representing above set using Venn diagram as follows:
∴ By Venn diagram,
Which one of the following is false?
In option (c), the set of all strings over a finite alphabet ∑ doesn’t forms a group under concatenation because the inverse of a string doesn’t exist with respect to concatenation.
The binary relation R = {(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)},on the set A = {1 , 2 , 3, 4} is
The relation R doesn’t contain (4, 4), so R is not reflexive relation.
Since relation R contains ( 1 ,1 ) , (2, 2) and (3, 3).
Therefore, relation R is also not irreflexive.
That R is transitive, can be checked by systematically checking for all (a, b) and (b, c) in R, whether (a, c) also exists in R.
Let' P(S) denote the power set of a set S. Which of the following is always true?
φ always present in any powerset of a set and φ is the only common element between P(S) and P(P(S)
Consider the set ∑* of all strings over the alphabet ∑ = {0,1}. ∑* with the concatenation operator for strings
Consider the binary relation:
S = {(x, y)  y = x + 1 and x, y ∈ {0, 1, 2, ...}}
The reflexive transitive closure of S is
In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Data Structures and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses. How many students have not taken any of the three courses?
According to inclusion  exclusion formula:
PL = students who have taken programming.
DS = Students who have taken Data structures.
CO = Students who have taken Computer Organization.
So, the number of students who have taken atleast 1 of the 3 courses is given by:
= 125 + 85 + 65  50  35  30 + 15
= 175
Therefore, the number of students who have not taken any of the 3 courses is
= Total studentsstudents taken atleast 1 course
= 200175 = 25
Let A, B and C be nonempty sets and let X = (A  B ) C and Y = (A  C)  (B  C) Which one of the following is TRUE?
The set {1, 2, 4, 7, 8,11,13,14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively
A relation R fs defined on ordered pairs of integers as follows: (x, y) R (u, v) if x < u and y > v. Then R is
Let P, Q and R be sets let A denote the symmetric difference operator defined as PΔG = ( P ∪ Q)  (P ∩ Q). Using Venn diagrams, determine which of the following is/are TRUE?
P Δ Q = PQ' + PQ
where Δ is symmetric difference between P and Q.
1.
2.
Consider the binary relation: R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE?
∴ R is not antisymmetric.
R is neithersymmetric nor antisymmetric.
How many onto (or surjective) functions are there from an nelement (n ≥ 2) set to a 2element set?
Let n = 2. There are only 2 onto functions as shown below:
The number of onto functions from a set A with m elements to set B with n elements where n < m is given by
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 








