1) What is meant by Boolean algebra?
2) How many 5-digit numbers can be formed using the digits 1,2,3,4,5,6,7, if digits cannot
be repeated, if digits can be repeated.
3) Prove that f(x)=2x+3 is a bijection from R to R. Find its inverse function.
4) Define an equivalence relation.
5) Define transitive closure of a relation with an example.
6) State Semi Group with example.
7) What is a lattice? Provide an example.
8) What is a reflexive relation? Give an example.
9) If A = {a, b, c, d} and B = {e, f, c, g}, find A∪B, A∩B, A−B and B−A.
10) Draw the Hasse diagram for the set B = {1,2,4,8,16} under the divisibility relation (a/b).
11) How many ways can the letters of the word ENGINEERING be arranged such that no two
vowels are adjacent?
12) Let A = {1,2,3,4}, B = {3,4,5,6}, and define R = {(a, b) | a ∈ A, b ∈ B, a < b}. Is R reflexive,
symmetric, or transitive?
13) Find the number of ways to arrange the letters in the word "MATHEMATICS" such that
the vowels appear together.
14) Let A = {1,2,3} and define a relation R on A as R = {(x, y):x divides y}. Determine if R is
reflexive, symmetric, and transitive. Explain the difference between symmetric and
antisymmetric relations. Give an example of a relation that is Symmetric but not
antisymmetric, Antisymmetric but not symmetric.
15) If U = {1,2,3,4,5,6,7} A = {1,2,3}, and B = {3,4,5}. Find Ac and Bc (complements of A and B
respectively). Verify (A∪B)c = Ac ∩ Bc.
16) Define Graph.
17) Define the symmetric difference of two sets A and B and prove that it is commutative.
18) Let A = Q (rational numbers) and define R on A such that if a−b is divisible by 4. Prove
that R is an equivalence relation and find all equivalence classes.
19) Define a function. Explain the difference between injective, surjective, and bijective
functions.
20) What is a bijection?
21) State the principle of inclusion-exclusion.
22) Prove that the intersection of two equivalence relations is also an equivalence relation.
23) In a group of 100 students, 60 like Mathematics, 50 like Physics, 30 like both
Mathematics and Physics. Find how many students like only Mathematics, only Physics,
and neither subject.
24) State Principle of Mathematical Induction.
25) Is ‘-‘ a binary operation on Natural Numbers.
26) Define a set.
27) If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4} and B = {3,4,5,6} find A∪B, A∩B, Ac, Ac ∩ Bc.
28) Define a relation R on A = {1,2,3,4} such that aRb if a+b is even. Determine whether R is
reflexive, symmetric, and transitive.
2) How many 5-digit numbers can be formed using the digits 1,2,3,4,5,6,7, if digits cannot
be repeated, if digits can be repeated.
3) Prove that f(x)=2x+3 is a bijection from R to R. Find its inverse function.
4) Define an equivalence relation.
5) Define transitive closure of a relation with an example.
6) State Semi Group with example.
7) What is a lattice? Provide an example.
8) What is a reflexive relation? Give an example.
9) If A = {a, b, c, d} and B = {e, f, c, g}, find A∪B, A∩B, A−B and B−A.
10) Draw the Hasse diagram for the set B = {1,2,4,8,16} under the divisibility relation (a/b).
11) How many ways can the letters of the word ENGINEERING be arranged such that no two
vowels are adjacent?
12) Let A = {1,2,3,4}, B = {3,4,5,6}, and define R = {(a, b) | a ∈ A, b ∈ B, a < b}. Is R reflexive,
symmetric, or transitive?
13) Find the number of ways to arrange the letters in the word "MATHEMATICS" such that
the vowels appear together.
14) Let A = {1,2,3} and define a relation R on A as R = {(x, y):x divides y}. Determine if R is
reflexive, symmetric, and transitive. Explain the difference between symmetric and
antisymmetric relations. Give an example of a relation that is Symmetric but not
antisymmetric, Antisymmetric but not symmetric.
15) If U = {1,2,3,4,5,6,7} A = {1,2,3}, and B = {3,4,5}. Find Ac and Bc (complements of A and B
respectively). Verify (A∪B)c = Ac ∩ Bc.
16) Define Graph.
17) Define the symmetric difference of two sets A and B and prove that it is commutative.
18) Let A = Q (rational numbers) and define R on A such that if a−b is divisible by 4. Prove
that R is an equivalence relation and find all equivalence classes.
19) Define a function. Explain the difference between injective, surjective, and bijective
functions.
20) What is a bijection?
21) State the principle of inclusion-exclusion.
22) Prove that the intersection of two equivalence relations is also an equivalence relation.
23) In a group of 100 students, 60 like Mathematics, 50 like Physics, 30 like both
Mathematics and Physics. Find how many students like only Mathematics, only Physics,
and neither subject.
24) State Principle of Mathematical Induction.
25) Is ‘-‘ a binary operation on Natural Numbers.
26) Define a set.
27) If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4} and B = {3,4,5,6} find A∪B, A∩B, Ac, Ac ∩ Bc.
28) Define a relation R on A = {1,2,3,4} such that aRb if a+b is even. Determine whether R is
reflexive, symmetric, and transitive.
