Math 300A

Reading Assignment: Read the rest of Chapter 2 and all of Chapter 3 in Gemignani

Assignment 2 (due in class Wednesday, 1/19))

Part A. Problems from Gemignani

For the odd problems, short versions of the answers are in the back of the book, so your answer should fill in the details as if you had not see that answer.

Section 2.6: #1, 2, 3, 4, 5, 6

Section 3.1: Study #1 carefully, but do not turn it in.

Do write up and turn in #2, 3, 4 (For example, for 3(a), let A be the statement "I (will) go" and B be "you (will) go". Then write each of the two statements to be investigated in (a) in terms of A and B – in this case "If A then B" and "If not B then not A", etc. Do something like this for the other cases as well.)

Section 3.2: #4

Part B. Contrapositive

For each statement below, write the contrapositive.

a) All equilateral triangles are isosceles

b) Any two equilateral triangles are similar.

c) For real numbers a, b, c, if a = b then ac = bc.

d) In a right triangle, two angles are complementary.

e) For integers m and n, if the sum m+n is even then m and n are both odd or m and n are both even.

Part C. NAND

Some mathematicians write A|B to mean "A and B are not both true".

a) Make a truth table for A|B.

b) Find a formula using only the connectives "and" , "or" and "not" that is equivalent to A|B.