Math 131A Lecture 2
Homework 1 – Due Apr. 6
Note: Group work is permitted on the homework provided that each person
writes their own answer in their own words. However, to obtain any major
benefit from the homework, it is recommended that the student spend significant
time and effort attempting each problem before collaborating or seeking help
from the teacher/teaching assistant/other students.
Problem 1: Using a truth table, verify that for any mathematical propositions
P, Q the following mathematical propositions are true (De Morgan’s laws for ∧,∨):
∼(P∧Q)⇔((∼P)∨(∼Q))
∼(P∨Q)⇔((∼P)∧(∼Q))
Problem 2: Using a truth table, verify that for any mathematical propositions
P, Q, R the following mathematical propositions are true (distributive laws for
∧,∨):
(P∧(Q∨R)) ⇔((P∧Q)∨(P∧R))
(P∨(Q∧R)) ⇔((P∨Q)∧(P∨R))
Problem 3: Using a truth table, verify that for any mathematical propositions
P, Q, R the following mathematical proposition is true (this demonstrates the va-
lidity of proof by contradiction):
(P⇒Q)⇔((P∧(∼Q)) ⇒(R∧(∼R)))
From the textbook:
Section 1.1: #1.3,1.4,1.7
Challenge Problem (Don’t turn it in): Section 1.1 #1.12.