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Consider the statements: p : You will ...

Consider the statements:
p : You will work hard q : You will become wealthy.
Translate each of the symbolic statements into an English sentence.
qimplies p

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The correct Answer is:
To solve the problem, we need to translate the symbolic statement \( q \implies p \) into an English sentence using the definitions of \( p \) and \( q \). 1. **Identify the statements:** - Let \( p \) represent the statement "You will work hard." - Let \( q \) represent the statement "You will become wealthy." 2. **Understand the implication:** - The expression \( q \implies p \) translates to "If \( q \) is true, then \( p \) is also true." - In English, this means "If you will become wealthy, then you will work hard." 3. **Write the final translation:** - Therefore, the symbolic statement \( q \implies p \) translates to: "If you will become wealthy, then you will work hard." ### Summary of the Solution: The translation of the symbolic statement \( q \implies p \) is: "If you will become wealthy, then you will work hard."
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ICSE-MATHEMATICAL REASONING-EXERCISE 27 (F)
  1. Write the converse of each of the following statements, In which cases...

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  2. Consider the statements: p : You will work hard q : You will becom...

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  3. Consider the statements: p : You will work hard q : You will becom...

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  4. Consider the statements: p : You will work hard q : You will becom...

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  5. Consider the statements: p : You will work hard q : You will becom...

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  6. Compare the following statements : p, only if q.

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  7. Compare the following statements : p implies q

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  8. Compare the following statements : p is a sufficient condition for q...

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  9. Compare the following statements : q is a necessary condition for p.

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  10. Compare the following statements : p, only if q.

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  11. Construct truth tables for the following : (p implies q)^^(qimplies...

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  12. Construct truth tables for each of the following : qimplies [(~p)vv...

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  13. Construct truth tables for each of the following : [(~p)^^ q]implies...

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  14. Write the converse, inverse and contrapositive for the statement (~p)i...

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  15. Write the inverse of the converse of p implies q.

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  16. Write the converse of the inverse of p implies q.

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  17. Write the contrapositive of the inverse of p implies q .

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  18. Write the converse of the contrapositive of p implies q .

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

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  20. What is the relationship of each resulting condition inverse , contatp...

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