Discrete Mathematics Answers

There are 7 groups in a picnic who has brought their own lunch box, and then the 7 lunch box are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their own.

Determine the truth values of each proposition below.
(a) 1 + 1 = 3 if and only if 2 + 2 = 3.
(b) If 1 + 1 = 2 or 1 + 1 = 3, then 2 + 2 = 3 and 2 + 2 = 4.
(c) If squirrels play badminton, then cats can’t fly.

. Let p and q be the propositions ”Swimming at the Sarıyer shore is allowed” and ”Sharks have been spotted near the shore”, respectively.
Express each of these compound propositions as an English sentence.
(a) ¬p ∨ q
(b) p ⇒ ¬q
(c) p ⇔ ¬q

Suppose that the statement p→ ¬q is false. Find all combinations of truth values of r and s for which (¬q→r)∧(¬p∨s) is true.

In a survey, 2000 people were queried if they read India Today or Business Times. It
was found 1200 read India Today, 900 read Business Times and 400 read both. How
many read at least one magazine

Prove that (1 * 2) + (2 * 3) + (3 * 4) + (4 * 5) + ....+ n (n + 1) = n (n + 1) (n + 2) / 3 for n positive integers

Write the following sets in the roster/tabular form:
a. G = {x : x ∈ N, 5 < x < 12}
b. H = {x : x is a multiple of 3 and x < 21}
c. I = {x : x is perfect cube 27 < x < 216}
d. J = {x : x = 5n - 3,n ∈ W, and n < 3}

1. Discuss two real world binary problems in two different fields using applications of Boolean Algebra.