Suppose A and B are 2 sets in a universal set U. The definition subsets is: We say that A is a subset of B (AC B) if and only if: Vx E U, if x E A then x E B Write the negation of the universal conditional statement in the definition: That is write what it means to say that A is not a subset of B (A ¢B):

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Discrete math proof:

please help with this proof regarding subsets. 

thank you so much! 

**Definition of Subsets**

Suppose \( A \) and \( B \) are two sets in a universal set \( U \). The definition of subsets is as follows:

We say that \( A \) is a subset of \( B \) (\( A \subseteq B \)) if and only if:

\[ \forall x \in U, \text{ if } x \in A \text{ then } x \in B \]

**Negation of the Universal Conditional Statement**

Write the negation of the universal conditional statement in the definition. That is, write what it means to say that \( A \) is not a subset of \( B \) (\( A \nsubseteq B \)):
Transcribed Image Text:**Definition of Subsets** Suppose \( A \) and \( B \) are two sets in a universal set \( U \). The definition of subsets is as follows: We say that \( A \) is a subset of \( B \) (\( A \subseteq B \)) if and only if: \[ \forall x \in U, \text{ if } x \in A \text{ then } x \in B \] **Negation of the Universal Conditional Statement** Write the negation of the universal conditional statement in the definition. That is, write what it means to say that \( A \) is not a subset of \( B \) (\( A \nsubseteq B \)):
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