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Compare the following statements : p i...

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

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To compare the statement "p is a sufficient condition for q," we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Statement**: - The statement "p is a sufficient condition for q" implies that if p is true, then q must also be true. This is a fundamental concept in logic. 2. **Expressing in Logical Terms**: - We can express this relationship in logical terms as: \[ p \implies q \] - This means that whenever p occurs, q will also occur. 3. **Identifying the Equivalent Statement**: - The phrase "p is a sufficient condition for q" can be rephrased as: - "If p, then q." - This is equivalent to the logical implication we wrote earlier. 4. **Conclusion**: - Therefore, we conclude that the statement "p is a sufficient condition for q" is equivalent to saying: \[ \text{If } p, \text{ then } q. \] ### Final Answer: The statement "p is a sufficient condition for q" is equivalent to "If p, then q." ---
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ICSE-MATHEMATICAL REASONING-EXERCISE 27 (F)
  1. Consider the statements: p : You will work hard q : You will becom...

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

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  5. Compare the following statements : p implies q

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. determine whether of the following two arguments is valid ? Given : ...

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  20. Determine whether of the following two arguments is valid ? Given : ...

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