Question

Select the correct alternative from given choices. The negation of a statement, 'If you are lazy, then you won't get the marks', is (A) 'You are not lazy or you wont get the marks.' (B) 'You are lazy or you will get the marks.' (C) 'You are lazy and you will get the marks.' (D) 'You are not lazy and you will get the marks.'

Name: Problem 3, Chapter 4: Computer Science and Information Technology
Uploaded: 2023-01-18T20:09:27-08:00
Duration: 1 min 35 s
Channel: Vysakh M
Description: Select the correct alternative from given choices. The negation of a statement, 'If you are lazy, then you won't get the marks', is (A) 'You are not lazy or you wont get the marks.' (B) 'You are lazy or you will get the marks.' (C) 'You are lazy and you will get the marks.' (D) 'You are not lazy and you will get the marks.'

   Select the correct alternative from given choices.
The negation of a statement, 'If you are lazy, then you won't get the marks', is
(A) 'You are not lazy or you wont get the marks.'
(B) 'You are lazy or you will get the marks.'
(C) 'You are lazy and you will get the marks.'
(D) 'You are not lazy and you will get the marks.'

Computer Science and Information Technology

Trishna Knowledge… 2018 Edition

Chapter 4, Problem 3

Instant Answer

Solved by Expert Vysakh M

01/18/2023

Step 1

This is a conditional statement of the form 'If P, then Q', where P is 'you are lazy' and Q is 'you won't get the marks'. Show more…

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Select the correct alternative from given choices. The negation of a statement, 'If you are lazy, then you won't get the marks', is (A) 'You are not lazy or you wont get the marks.' (B) 'You are lazy or you will get the marks.' (C) 'You are lazy and you will get the marks.' (D) 'You are not lazy and you will get the marks.'

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Key Concepts

Negation of a Conditional Statement

Negating a conditional statement like 'if P then Q' involves identifying the conditions under which the original statement fails. Since 'if P then Q' is equivalent to 'not P or Q', its negation becomes 'P and not Q', meaning that the antecedent is true while the consequent is false.

Logical Equivalences

Logical equivalences allow rewriting logical expressions in different forms that have the same truth values. Knowing that an implication can be expressed as 'not P or Q' and understanding how to negate it using these equivalences is a key tool in propositional logic.

Implication

An implication, or conditional statement, is a logical construct typically phrased as 'if P then Q'. It is considered false only when the antecedent (P) is true and the consequent (Q) is false, and true in all other cases.

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