Let A = {1,5,6,7,8,10}, B = {1,4,5,9} and C = {1,4,6,7,9} then verify that A∪(B∩C) = (A∪B)∩(A∪C)05
[5 marks]5+√2 i Express in the form a+ib. 1−√2 i05
[ marks]Define: 1) Regular graph 2) Complete graph
[5 marks]Let f:A → B, where A = {1,2,3},B = {1,2,3,4,5,6,7,8,9,10}, and f(x) = x2 −2x +3; find the domain, co-domain, and range of f.
[ marks]Solve: x2 +2x+4 = 0
[5 marks]State and prove D’Morgan’s laws in Boolean algebra.
[5 marks]Solve the system of equations using the matrix method: 2x +5y = 1 3x +2y = 705
[5 marks]05 List various types of matrices with appropriate examples for each.
[ marks]Find the unit vector in the direction of a = 2i+3j+k.
[ marks]Find the values of x such that: 3 x 3 | | = | | x 1 4 1
[2 marks]05 Find the area of the triangle with vertices (3,8),(−4,2) and (5,1).
[ marks]Calculate the mean deviation from the mean for the given data. Markes obtained 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Number of students 2 3 8 14 8 3
[2 marks]Explain combination and permutations with examples.
[5 marks]05 Explain the concept of the degree of vertex in detail with a suitable example.
[ marks]Acommittee of people is chosen from two men and two women. What is the probability that the committee will have:
[5 marks]no man?
[ marks]one man?
[ marks]two men? OR05
[ marks]Use a truth table to prove that (A+B).(A+C) = A+(B.C)
[ marks]Write the truth table for the compound proposition p∧(q ∨r) ↔ [(p∧q)∨(p∧r)].
[5 marks]