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Statements: Either P marris Q or X marris Y
Among the options below, the logical NEGATION of the above statement is :
Among the options below, the logical NEGATION of the above statement is :
- a)Neither P marries Q nor X marries Y.
- b)P does not marry Q and X marries Y.
- c)P marries Q and X marries Y.
- d)X does not marry Y and P marries Q.
Correct answer is option 'C'. Can you explain this answer?
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Statements: Either P marris Q or X marris Y Among the options below, t...
As we are directed to do logical negation, of given statement, situation of “either or” will becomes “Neither nor”
Hence, the correct option is (C).
Hence, the correct option is (C).
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Statements: Either P marris Q or X marris Y Among the options below, t...
Logical Negation of the Statement:
The logical negation of the statement "Either P marries Q or X marries Y" is given as option c) "P marries Q and X marries Y."
Explanation:
To understand why option c) is the correct logical negation of the given statement, let's break down the original statement and analyze its negation.
Original Statement:
Either P marries Q or X marries Y
Analysis:
The original statement presents a disjunction, which means it is true if either one of its two parts is true. So, the original statement is true in two cases:
1. P marries Q, and X does not marry Y.
2. X marries Y, and P does not marry Q.
Logical Negation:
The negation of a disjunction is a conjunction.
Explanation of Option c) "P marries Q and X marries Y":
The negation of the original statement can be written as:
- It is not the case that either P marries Q or X marries Y.
This can be further simplified as:
- P does not marry Q and X does not marry Y.
Explanation of Incorrect Options:
a) Neither P marries Q nor X marries Y: This option is incorrect because it represents the negation of the original statement as a conjunction. It states that neither P marries Q nor X marries Y, which is not the logical negation of the original disjunction.
b) P does not marry Q and X marries Y: This option is incorrect because it only negates the first part of the original disjunction. It states that P does not marry Q, but it does not specify the status of X marrying Y.
d) X does not marry Y and P marries Q: This option is incorrect because it only negates the second part of the original disjunction. It states that X does not marry Y, but it does not specify the status of P marrying Q.
Conclusion:
Among the given options, option c) "P marries Q and X marries Y" is the correct logical negation of the original statement "Either P marries Q or X marries Y." It accurately represents the negation as a conjunction, indicating that both P marries Q and X marries Y must be true for the negation to hold.
The logical negation of the statement "Either P marries Q or X marries Y" is given as option c) "P marries Q and X marries Y."
Explanation:
To understand why option c) is the correct logical negation of the given statement, let's break down the original statement and analyze its negation.
Original Statement:
Either P marries Q or X marries Y
Analysis:
The original statement presents a disjunction, which means it is true if either one of its two parts is true. So, the original statement is true in two cases:
1. P marries Q, and X does not marry Y.
2. X marries Y, and P does not marry Q.
Logical Negation:
The negation of a disjunction is a conjunction.
Explanation of Option c) "P marries Q and X marries Y":
The negation of the original statement can be written as:
- It is not the case that either P marries Q or X marries Y.
This can be further simplified as:
- P does not marry Q and X does not marry Y.
Explanation of Incorrect Options:
a) Neither P marries Q nor X marries Y: This option is incorrect because it represents the negation of the original statement as a conjunction. It states that neither P marries Q nor X marries Y, which is not the logical negation of the original disjunction.
b) P does not marry Q and X marries Y: This option is incorrect because it only negates the first part of the original disjunction. It states that P does not marry Q, but it does not specify the status of X marrying Y.
d) X does not marry Y and P marries Q: This option is incorrect because it only negates the second part of the original disjunction. It states that X does not marry Y, but it does not specify the status of P marrying Q.
Conclusion:
Among the given options, option c) "P marries Q and X marries Y" is the correct logical negation of the original statement "Either P marries Q or X marries Y." It accurately represents the negation as a conjunction, indicating that both P marries Q and X marries Y must be true for the negation to hold.
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Statements: Either P marris Q or X marris Y Among the options below, the logical NEGATION of the above statement is :a)Neither P marries Q nor X marries Y.b)P does not marry Q and X marries Y. c)P marries Q and X marries Y.d)X does not marry Y and P marries Q.Correct answer is option 'C'. Can you explain this answer?
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