7/24/2019 cogs502-hw2-2015-Fall

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Cogs 502 Prog. & Log.

Fall 2015 Homework 2 Due 29 Oct 2015, 9am

Question 1 (20%)

Let A = {1,2,3}. Write all the functions f :A A, indicating which ones are one-to-one correspon-dences.

Question 2 (20%)

LetR= {(a,b),(a,c),(c,d),(a,a),(b,a)}. What is the composition R R? What is R1? IsR,R RorR1 a function?

Question 3 (20%)

Give a setA such that there exists an a where botha Aand a A.

Question 4 (20%)

LetA be a non-empty set and let R AAbe the empty set. Which properties does R have?

(a) Reflexivity

(b) Symmetry

(c) Anti-symmetry

(d) Transitivity

Question 5 (20%)

Let Cbe a set of sets defined as follows:

i. /0 C

ii. IfS1 Cand S2C, then {S1,S2} C.

iii. IfS1 Cand S2C, thenS1S2 C.

iv. Nothing else is in C.

(a) Explain step-by-step why {/0,{/0}} C(b) Give an example of a setSof ordered pairs such that SCand |S|>1.