Discrete Mathematics Answers

1.  Let A = {c, n, b}, B = {x, y} and C = {0, 1}.

Find

a)   A X B X C

b)   C X B X A

c)   B X C X C 

1. Determine whether these functions are onto, one-to-one, both or neither. Justify your answer.

a)   f(1) = c, f(2) = d, f(3) = a, f(4) = d, f(5) = b

b)   g(1) = d, g(2) = c, g(3) = a, g(4) = b

c)   h(1) = b, h(2) = d, h(3) = b, h(4) = c

Prove or disprove that the two propositions in each pair are equivalent.

 ((p "\\leftrightarrow" q) "\\leftrightarrow" r), (p "\\leftrightarrow" (q "\\leftrightarrow" r))

Prove or disprove that the two propositions in each pair are equivalent.

 (p "\\bigoplus" (q "\\to" r)), ((p "\\bigoplus" q) "\\to" (p "\\bigoplus" r))

1.  Prove or disprove that the two propositions in each pair are equivalent.

a)   (p "\\to" (q "\\to" r)) , ((p "\\to" q ) "\\to" ( p "\\to" r ))

Give the inverse, converse and contrapositive for each of the following propositions.

a) If x + y = 1 then x2 + y2 ≥ 1

b) If 2 + 2 = 4 then 3 + 3 = 8

Determine whether the following are propositions. Give the truth value of the propositions.

a) Asia is the largest of the Earth’s seven continents.

b) 4 + x = 5

c) 2 * 3 = 5

d) Answer this question

e) The human heart is shaped like an upside-down pear and is located slightly to the left of center inside the chest cavity

Convert the following hexadecimal numbers to decimal numbers.

a) DE5₁₆

b) 2AB.4₁₆

Convert each of the following integers from binary notation to hexadecimal notation.

a) 101010101010

b) 111011101110111