Discrete Mathematics Answers

Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method. 

prove a --> ( b V c ) using contradiction method and combination of inference rules and equivalence laws from these premises : 1. a --> ( d V b ) 2. d --> c

The following table shows the income distribution of 600 families. Find the minimum income

of the riches 30% families. Also the limits of income of middle 50% of families, to the nearest

rupees.

Income Below

75

75-

150

150-

225

225-

300

300-

375

375-

400

400 &

above

No. of

families

69 137 225 46 88 25 10

Ans.: the richest 30 % families earns Rs. 222 and above per week , the middle 50% families

weekly income lies between 120 and 256.

Draw the Venn diagrams for each of these combinations of the sets A, B, and C.

A ∩ (B − C)

(A ∩ B) ∪ (A ∩ C)

(A ∩ ) ∪ (A ∩ )

Let A represent the set of all students at a university, and let B represent the set of all courses

offered at the university. What is the Cartesian product A × B and how can it be used?

What is the variable x after the statement -if2+3=6 if and only if 3+2=5, x = x+1^ - if x = 2 ?

Let p and q be propositions, construct the truth table for the compound proposition.

~(p^q)

Show that if A, B, and C are sets, then A ∩ B ∩ C = A ∪ B ∪ C

•by showing each side is a subset of the other side.

•using a membership table.

Venn diagram

(A ∩ B) ∪ (A ∩ C)

(A ∩ ) ∪ (A ∩ )