Let A = {4, 5, 7, 8, 10}, B = {4, 5, 9} and C = {1, 4, 6, 9} then verify that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
[5 marks]Give an example of relation which is reflexive and transitive but not symmetric.
[5 marks]Define simple graph and null graph with example.
[5 marks]Solve x2 – x + 2 = 0.
[5 marks]Express 1+i in terms of a + ib.05 3+2i
[ marks]3 x 3 Find value of x for which | | = | | x 1 4 1
[5 marks]Let f:A→Bwhere A = {1, 2, 3} and B = {1, 2, 3, 4, 5, 6, 7} f(x) = 2x then find domain, co-domain and range of f.
[5 marks]2 1 −2 If A = ⌈ ⌉ and B = ⌈4 5⌉ then find AB and BA. −4 2 521
[3 marks]2 0 −1 If A = ⌈5 1 0 ⌉ then find A−1, if it exist.013
[5 marks]Find mean deviation about mean for following data: xi 2 5 6 8 10 fi 2 8 10 7 8 51
[12 marks]Three unbiased coins are tossed. Find probability of (i) all heads (ii) atleast 2 heads (iii) atmost 2 heads. OR
[5 marks]Find standard deviation for following data: x 4 8 11 17 20 24 32 i fi 3 5 9 5 4 3 1
[ marks]Acard drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate probability that the card will be (i) a diamond (ii) a black card.
[5 marks]State Boolean Algebra with an example.
[5 marks]What is De Morgan’s law in Boolean Algebra. By using it, show equivalent expression for [(x. y) (z’ + xy’)] = x’ + y’ + z’.
[5 marks]What is logic gate? Mention about AND gate, OR gate and NOT gate.
[5 marks]Write truth table for compound proposition p ⋁ ( q ⋀ r )↔ [( p ⋁ q ) ⋀ ( p ⋁ r )]
[5 marks]