Relations and Functions - Inverse Relations Question

• Nov 13th 2011, 10:25 AM
maclunian
Relations and Functions - Inverse Relations Question
Let S = {a,b,c,d,e} be a set of senators and P = {w,x,y,z} be a set of policies. Let RCS*P be the relation defined by sRp if s supports p.

Q1: Define the inverse relation: R^(-1)

my answer: R^(-1) = {(p,s) (element of) P*S; (s,p) (element of) R}

Q2: What does pR^(-1)s mean?

my answer: pR^(-1) s means sRp

Q3: What is {s (element of) S; pR^(-1) s}

Don't know the answer to this one.

Are my first two answers correct, and how would I answer the third question? Thanks in advance.
• Nov 13th 2011, 12:20 PM
emakarov
Re: Relations and Functions - Inverse Relations Question
Quote:

Originally Posted by maclunian
Q1: Define the inverse relation: R^(-1)

my answer: R^(-1) = {(p,s) (element of) P*S; (s,p) (element of) R}

Correct.

Quote:

Originally Posted by maclunian
Q2: What does pR^(-1)s mean?

my answer: pR^(-1) s means sRp

I think the question asked to describe the relation $R^{-1}$ in words, similar to how $sRp$ means "s supports p."

Quote:

Originally Posted by maclunian
Q3: What is {s (element of) S; pR^(-1) s}

Don't know the answer to this one.

If you do Q2, then it is easy to describe the set $\{s\in S: pR^{-1}s\}$ in words for each particular $p$.