Question

Select the correct alternative from given choices. The negation of the statement 'All A's are B's' is (A) All A's are not B's. (B) Only one $\mathrm{A}$ which is not $\mathrm{B}$. (C) There is atleast one A which is B. (D) Some A's are not B's.

Name: Problem 4, Chapter 4: Computer Science and Information Technology
Uploaded: 2023-01-18T20:13:42-08:00
Duration: 1 min 9 s
Channel: Vysakh M
Description: Select the correct alternative from given choices. The negation of the statement 'All A's are B's' is (A) All A's are not B's. (B) Only one A which is not B. (C) There is atleast one A which is B. (D) Some A's are not B's.

   Select the correct alternative from given choices.
The negation of the statement 'All A's are B's' is
(A) All A's are not B's.
(B) Only one $\mathrm{A}$ which is not $\mathrm{B}$.
(C) There is atleast one A which is B.
(D) Some A's are not B's.

Computer Science and Information Technology

Trishna Knowledge… 2018 Edition

Chapter 4, Problem 4

Instant Answer

Solved by Expert Vysakh M

01/18/2023

Step 1

This means that every element in set A is also an element in set B. Show more…

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Select the correct alternative from given choices. The negation of the statement 'All A's are B's' is (A) All A's are not B's. (B) Only one $\mathrm{A}$ which is not $\mathrm{B}$. (C) There is atleast one A which is B. (D) Some A's are not B's.

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Key Concepts

Existential Quantification

Existential quantification is used to assert that there is at least one element in a domain for which a particular property is true. When a universal statement is negated, the resulting statement typically becomes an existential statement, indicating that the universal claim fails for at least one instance.

Universal Quantification

Universal quantification is a fundamental concept in predicate logic where a statement applies to every member of a domain. Statements like 'All A's are B's' assert that every element that qualifies as A must also satisfy property B.

Negation of Universal Statements

The negation of a universally quantified statement is achieved by replacing it with an existential quantifier and negating the predicate. This means that instead of claiming 'for all elements, property P holds', the negation claims 'there exists at least one element for which property P does not hold'.

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