**Set Theory - Expressions and Validity**Consider three sets $A$, $B$, and $C$, an object $x$, and statements $p$ and $q$. Evaluate the validity of each expression listed below, determining whether it makes sense (yes) or does not make sense (no). If an expression is valid, classify it as either a statement or a set. When invalid, briefly explain why.a) $x \in A$b) $p \in \mathbb{Z}$c) $A \in q$d) $\sim A$e) $x \in A \land B$f) $x \in A \lor q$g) $(A \cup B) \cap C$h) $A \cup B \subseteq C$i) $(x \in A)'$j) $x \in A^t$k) $\sim (x \in A) \cap B$l) $\sim (x \in A \cap B)$*Note: The symbol $\sim$ denotes 'not,' $\land$ denotes logical 'and,' $\lor$ denotes logical 'or,' $\cup$ denotes union, and $\cap$ denotes intersection.*

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2. Let A, B and C be sets, x an object, and p and g statements. For each expression given below, determine whether it makes sense (yes) or it does not make sense (no). If your answer is yes, state whether the expression is a statement or a set. If the answer is no. briefly explain why. a) xEA b) peZ c) Aeq V- (p g) (AUB)NC e) rEAAB i) (xE AY I)-(XEANB) h) AUBCC k) - (xE A)NB

2. Let A, B and C be sets, x an object, and p and g statements. For each expression given below, determine whether it makes sense (yes) or it does not make sense (no). If your answer is yes, state whether the expression is a statement or a set. If the answer is no. briefly explain why. a) xEA b) peZ c) Aeq V- (p g) (AUB)NC e) rEAAB i) (xE AY I)-(XEANB) h) AUBCC k) - (xE A)NB

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

**Set Theory - Expressions and Validity**

Consider three sets $A$, $B$, and $C$, an object $x$, and statements $p$ and $q$. Evaluate the validity of each expression listed below, determining whether it makes sense (yes) or does not make sense (no). If an expression is valid, classify it as either a statement or a set. When invalid, briefly explain why.

a) $x \in A$

b) $p \in \mathbb{Z}$

c) $A \in q$

d) $\sim A$

e) $x \in A \land B$

f) $x \in A \lor q$

g) $(A \cup B) \cap C$

h) $A \cup B \subseteq C$

i) $(x \in A)'$

j) $x \in A^t$

k) $\sim (x \in A) \cap B$

l) $\sim (x \in A \cap B)$

*Note: The symbol $\sim$ denotes 'not,' $\land$ denotes logical 'and,' $\lor$ denotes logical 'or,' $\cup$ denotes union, and $\cap$ denotes intersection.*

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