Q$7.(4$ pts$)$ Prove or disprove each of the following claims. In your justifications, you may refer to any of the facts

about cardinality we mentioned in class or that appear in the relevant sections in the textbook. Credit will be

given for correctness of the conclusion of each part, i$.$e$.$ whether claim is true or false, and fair effort in the

justification.

$7.$a$.$X in P$($R$)$Y in P$($R$)((|$X$|=|$Y $|)->($X $=$ Y $))$

$7.$b$.$A in P$($R$)$B in P$($R$)($ Z $$ A $$ Z $$ B $(|$A$|=|$B$|))$