91Ó°ÊÓ

The production rules of a grammar for simple arithmetic expressions are: $$\langle\text { expression }\rangle :=\langle\text { digit })(\langle\text { expression })) |+(\langle\text { expression }\rangle) |$$ $$-(\langle\text { expression }\rangle) | \langle\text { expression }\rangle \langle\text { operator }\langle\text { expression }\rangle$$ $$\langle\text { digit }\rangle : := 0|1| 2|3| 4|5| 6|7| 8 | 9$$ $$\langle\text { operator }\rangle : :=+|-| / | \uparrow$$ Use this grammar to answer Exercises \(52-59\). Determine if each is a valid arithmetic expression. $$3+\uparrow 7$$

Find three words belonging to each language over \(\sigma=\\{0,1\\}\). \\{0\\}\(\\{0,1\\}^{*}\\{1\\}\)

Find three words belonging to each language over \(\sigma=\\{0,1\\}\). \(\\{0\\}^{*}\\{1\\}^{*}\\{0\\}^{*}\)

Construct a derivation tree for each expression. $$3+5 * 6$$

Prove each, where \(A, B,\) and \(C\) are arbitrary languages over \(\Sigma\) and \(x \in \Sigma\). If \(A \subseteq B,\) then \(A^{n} \subseteq B^{n}\) for every \(n \geq 0\)

Construct a derivation tree for each expression. $$5+(4 \uparrow 3)$$

The production rules of a grammar for simple arithmetic expressions are: $$\langle\text { expression }\rangle :=\langle\text { digit })(\langle\text { expression })) |+(\langle\text { expression }\rangle) |$$ $$-(\langle\text { expression }\rangle) | \langle\text { expression }\rangle \langle\text { operator }\langle\text { expression }\rangle$$ $$\langle\text { digit }\rangle : := 0|1| 2|3| 4|5| 6|7| 8 | 9$$ $$\langle\text { operator }\rangle : :=+|-| / | \uparrow$$ Use this grammar to answer Exercises \(52-59\). Construct a derivation tree for each expression. $$5+(4 \uparrow 3)$$

Prove each, where \(A, B,\) and \(C\) are arbitrary languages over \(\Sigma\) and \(x \in \Sigma\). If \(A \subseteq B,\) then \(A^{*} \subseteq B^{*}\)

Construct a derivation tree for each expression. $$(5+3)-7 / 4$$

The production rules of a grammar for simple arithmetic expressions are: $$\langle\text { expression }\rangle :=\langle\text { digit })(\langle\text { expression })) |+(\langle\text { expression }\rangle) |$$ $$-(\langle\text { expression }\rangle) | \langle\text { expression }\rangle \langle\text { operator }\langle\text { expression }\rangle$$ $$\langle\text { digit }\rangle : := 0|1| 2|3| 4|5| 6|7| 8 | 9$$ $$\langle\text { operator }\rangle : :=+|-| / | \uparrow$$ Use this grammar to answer Exercises \(52-59\). Construct a derivation tree for each expression. $$(5+3)-7 / 4$$