Rose Harrison and Clara Huizink Solutions for Exercise 7: Practice 3

Determine whether the given statement is true or false. If the statement is false, give a reason why.

$\left\{4\right\}$ $\underline{\subset }\{2, 3, 4\}$

Determine whether the given statement is true or false. If the statement is false, give a reason why.

Given $A=\{\overline{)x}x\in Z, 1<x<5\}$ and $B=\{2, 3, 4\}$, then $A=B$.

Determine if the statement given below is true or false. If statement is false, give a counter-example (find an example that makes the statement false). You may find drawing a diagram helpful.

If $A\underline{\underline{\subset }} B$ and $B\underline{\subset } C$, then A$\underline{\underline{\subset }} C$

Determine if the statements given below are true or false. For those that are false, give a counter-example (find an example that makes the statement true). You may find drawing a diagram helpful.

If $R\underline{\underline{\subset }} S$ th en S$\underline{\underline{\subset }} R$

Determine if the statement given below are true or false. If the statement is false, give a counter-example (find an example that makes the statement true). You may find drawing a diagram helpful.

If p$\in$P and $P\underline{\subset } Q$ , then p$\in Q$

Determine if the statements given below are true or false. For those that are false, give a counter-example (find an example that makes the statement true). You may find drawing a diagram helpful.

If $A=B$ then B$\underline{\underline{\subset }} A$

Write a set that has $32$ subsets.

Determine whether or not a set can have exactly 24 subsets.