Question:
If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p,
q, r$ are respectively
If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p,
q, r$ are respectively
Updated On: May 19, 2024
- T, F, F
- F, F, F,
- F, T, T
- T, T,F
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The Correct Option is A
Approach Solution - 1
$p \Rightarrow q \vee r$ is false when $p$ is true and $q \vee r$ is false, and $q \vee r$ is false when both $q$ and $r$ are false.
Hence truth values of $p, q, r$ are respectively T, F, F
Hence truth values of $p, q, r$ are respectively T, F, F
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Approach Solution -2
The correct option is A)
p→q is false only while both p and q are true.
∴ p→(q∨r) When p is true and (qvr) is false, then
When both q and r are false, qr is false.
Hence T,F,F
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Concepts Used:
Statements
A statement is a sentence that is either true or false, but not both true and false simultaneously.
Types of Statements:
Simple Statement
- If a statement cannot be further broken down into various statements, or in simpler words if it is concrete by itself, it is called a Simple Statement.
- Examples include:
- A kite is not a rhombus.
- 15 is an odd number.
Compound Statement
- If a statement can further be broken down into simpler statements so that from a main statement, we can yield more than one statement, then it is called a Compound Statement.
- Consider the statement “10 is non-negative and a multiple of 5” which can be broken down into the statements: “10 is non-negative” and “10 is a multiple of 5”.
If-Then Statements
- If we encounter an if-then statement i.e. ‘if a then b’, then by proving that a is true, b can be proved to be true or if we prove that b is false, then a is also false.
- If we encounter a statement which says ‘a if and only if b’, then we can give reason for such a statement by showing that if a is true, then b is also true and if b is true, then a is also true.
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