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A compound statement with an ‘Or’ is false when both the component statements are ……
- a)Same
- b)True
- c)Different
- d)False
Correct answer is option 'D'. Can you explain this answer?
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A compound statement with an ‘Or’ is false when both the c...
Any compound statement which has And as the connecting word is said to be false if all its component statements are false. A compound statement which has Or as the connecting word is said to be true if one of its component statement orboth the component statements is true.
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A compound statement with an ‘Or’ is false when both the c...
Understanding Compound Statements with 'Or'
In logic, compound statements are formed by combining simpler statements. The logical 'Or' operator (denoted as ∨) plays a crucial role in determining the truth value of these statements.
Truth Values of 'Or'
An 'Or' statement is typically true in all cases except when both component statements are false. This can be summarized as follows:
- **True ∨ True** = True
- **True ∨ False** = True
- **False ∨ True** = True
- **False ∨ False** = False
Explanation of the Answer
Given the question, we need to identify when a compound statement using 'Or' is false. The only scenario in which this occurs is when both component statements are false.
Key Points:
- **Both Statements False**: If both component statements are false (False ∨ False), the entire compound statement evaluates to false.
- **Any True Statement**: If at least one of the statements is true, the compound statement will always be true (True ∨ False or True ∨ True).
Conclusion
Thus, the correct answer to the question is option 'D' (False). The understanding of how 'Or' operates is essential for solving logical expressions, especially in JEE-level problems. Remember that a compound statement with 'Or' is only false when both components are false.
In logic, compound statements are formed by combining simpler statements. The logical 'Or' operator (denoted as ∨) plays a crucial role in determining the truth value of these statements.
Truth Values of 'Or'
An 'Or' statement is typically true in all cases except when both component statements are false. This can be summarized as follows:
- **True ∨ True** = True
- **True ∨ False** = True
- **False ∨ True** = True
- **False ∨ False** = False
Explanation of the Answer
Given the question, we need to identify when a compound statement using 'Or' is false. The only scenario in which this occurs is when both component statements are false.
Key Points:
- **Both Statements False**: If both component statements are false (False ∨ False), the entire compound statement evaluates to false.
- **Any True Statement**: If at least one of the statements is true, the compound statement will always be true (True ∨ False or True ∨ True).
Conclusion
Thus, the correct answer to the question is option 'D' (False). The understanding of how 'Or' operates is essential for solving logical expressions, especially in JEE-level problems. Remember that a compound statement with 'Or' is only false when both components are false.
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A compound statement with an ‘Or’ is false when both the component statements are ……a)Sameb)Truec)Differentd)FalseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A compound statement with an ‘Or’ is false when both the component statements are ……a)Sameb)Truec)Differentd)FalseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A compound statement with an ‘Or’ is false when both the component statements are ……a)Sameb)Truec)Differentd)FalseCorrect answer is option 'D'. Can you explain this answer?.
A compound statement with an ‘Or’ is false when both the component statements are ……a)Sameb)Truec)Differentd)FalseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A compound statement with an ‘Or’ is false when both the component statements are ……a)Sameb)Truec)Differentd)FalseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A compound statement with an ‘Or’ is false when both the component statements are ……a)Sameb)Truec)Differentd)FalseCorrect answer is option 'D'. Can you explain this answer?.
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