# \displaystyle\text{Let}{U}={\left\lbrace{p},{q},{r},{s},{t}\right\rbrace},{D}={\left\lb

$$\displaystyle\text{Let}{U}={\left\lbrace{p},{q},{r},{s},{t}\right\rbrace},{D}={\left\lbrace{p},{r},{s},{t}\right\rbrace},{E}={\left\lbrace{q},{s}\right\rbrace},{F}={\left\lbrace{p},{r}\right\rbrace},{\quad\text{and}\quad}{G}={\left\lbrace{s}\right\rbrace}$$
Determine whether the statement is true or false. $$F \subset D$$

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un4t5o4v

$$\displaystyle{\left\lbrace{p},{t}\right\rbrace}\subset{\left\lbrace{p},{r},{s},{t}\right\rbrace}\Rightarrow{F}\subset{D}$$
This is because:$$\displaystyle{F}={\left\lbrace{p},{t}\right\rbrace}{\quad\text{and}\quad}{D}{\left\lbrace{p},{r},{s},{t}\right\rbrace}$$ as all elements in set F exist in that of set D, F is a subset of D
$$\displaystyle\therefore{T}{r}{u}{e}$$