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Consider the following statements P : ...

Consider the following statements
P : I have the raincoat q : I can walk in the rain.
The propositions " If i have the raincoat , then I can walk in the rain " is represented by

A

`p to q `

B

p v q

C

p ^ q

D

` p harr q`

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AI Generated Solution

The correct Answer is:
To solve the problem, we need to represent the given propositions using logical notation. ### Step-by-Step Solution: 1. **Identify the Statements**: - Let \( P \): "I have the raincoat." - Let \( Q \): "I can walk in the rain." 2. **Understand the Implication**: - The statement "If I have the raincoat, then I can walk in the rain" can be expressed in logical terms as an implication. In logic, the implication is denoted by the symbol \( \rightarrow \). 3. **Formulate the Implication**: - The implication can be written as: \[ P \rightarrow Q \] This reads as "If \( P \) (I have the raincoat), then \( Q \) (I can walk in the rain)." 4. **Conclusion**: - Therefore, the proposition "If I have the raincoat, then I can walk in the rain" is represented by \( P \rightarrow Q \). ### Final Answer: The correct representation of the statement is \( P \rightarrow Q \). ---

To solve the problem, we need to represent the given propositions using logical notation. ### Step-by-Step Solution: 1. **Identify the Statements**: - Let \( P \): "I have the raincoat." - Let \( Q \): "I can walk in the rain." ...
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OBJECTIVE RD SHARMA ENGLISH-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. Consider the following propositions : p : To become on airfore office...

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  2. Conider the following is statements : p : A parallelogram is a rhomb...

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  3. Consider the following statements P : I have the raincoat q : I can ...

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  4. Which of the following is true for the propositions p and q ?

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  5. Consider the following propositions : P : It rains ,q : Then stree...

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  6. The logically equvalent proposition of p harr q is

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  7. Using truth table show that - (p vv q) vv (~ p ^^ q ) is logically eq...

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  8. The inverse of the proposition (p^^~q) to r is

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  9. Logical equivalent propostion to the proposition ~ ( p ^^ q) is

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  10. Which of the following is logically equivalent to ( p^q) ?

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  11. Write the contrapositive of the contrapositive of p implies q.

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  12. The expression ~(~p rarr q) is logically equivalent to

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  13. The logically equivalent proposition of p harr q is

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  14. If p to (qvvr) is false, then the truth values of p,q, and r are, res...

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  15. The compound statement p to ( ~ p ^^ q) is false, then the truth va...

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  16. The false statement in the following is

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  17. Which of the following is a proposition ?

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  18. (p^^~q)^^(~p^^q) is

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  19. The proposition (p to ~p) ^^ (~p to p) is a

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  20. Which of the following statements is a tautology?

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