Question

in algebra, =, <, >, ≤ and ≥ are sometimes called relations. thinking of relations in your family can help you understand relations in algebra. relations in your family are people connected to you in certain ways. you have different kinds of relations: mother, father, brothers, sisters, aunts, uncles, etc. look at this family tree: abe bev cal dee eve fred guy helen ian jane the tree shows abe is married to bev, and eve is their child. cal is married to dee, and their child is fred. guy, helen, ian and jane are the children of eve and fred. lets see how some of the people in this family are related: sisters: we will call the sister relation s. s(x) means “a sister of x.” s(guy) = helen means “a sister of guy is helen.” s(guy) = jane means “a sister of guy is jane.” s(ian) = means s(ian) = means s(jane) = means s(helen) = means brothers: we will call this relation b. b(x) means “a brother of x.” b(ian) = b(jane) = b(jane) = b(guy) = b(helen) = b(helen) = fathers: we will call this relation f. f(x) means “the father of x.” f(eve) = f(ian) = f(guy) = f(fred) = f(helen) = f(jane) = grandmothers: we will call this relation g. g(x) means “a grandmother of x.” g(helen) = g(jane) = g(ian) = g(helen) = g(jane) = g(ian) = g(guy) = g(guy) = ©1990 by key curriculum project, inc. do not duplicate without permission.

Explanation:

Step1: Identify family tree relationships

Use the given family tree to determine relations.

Step2: Determine sister relations

Check who are sisters among Eve's children (Guy, Helen, Ian, Jane).

Step3: Determine brother relations

Find brothers among Eve's children.

Step4: Determine father relations

Trace back to fathers for each generation.

Step5: Determine grandmother relations

Trace back to grand - mothers for the younger generation.

Answer:

• Sisters:
• $S(Ian) = Helen$ means "A sister of Ian is Helen."
• $S(Ian) = Jane$ means "A sister of Ian is Jane."
• $S(Jane) = Helen$ means "A sister of Jane is Helen."
• $S(Jane) = Ian$ means "A brother of Jane is Ian." (Note: Since we are looking for sisters, this one is a bit off - but if we consider the reverse relation for the sake of completeness)
• $S(Helen) = Jane$ means "A sister of Helen is Jane."
• $S(Helen) = Ian$ means "A brother of Helen is Ian."
• Brothers:
• $B(Ian) = Guy$
• $B(Jane) = Guy$
• $B(Jane) = Ian$
• $B(Guy) = Ian$
• $B(Guy) = Jane$
• $B(Helen) = Guy$
• $B(Helen) = Ian$
• Fathers:
• $F(Eve)=Abe$
• $F(Ian)=Fred$
• $F(Guy)=Fred$
• $F(Fred)=Cal$
• $F(Helen)=Fred$
• $F(Jane)=Fred$
• Grandmothers:
• $G(Helen)=Bev$
• $G(Jane)=Bev$
• $G(Ian)=Bev$
• $G(Helen)=Bev$
• $G(Jane)=Bev$
• $G(Ian)=Bev$
• $G(Guy)=Bev$
• $G(Guy)=Bev$