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 R__C__S*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.

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 $\displaystyle R^{-1}$ in words, similar to how $\displaystyle sRp$ 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 $\displaystyle \{s\in S: pR^{-1}s\}$ in words for each particular $\displaystyle p$.