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From the biconditional statement p h...

From the biconditional statement ` p harrq`, where.
(i) p: The units digits of an interger is zero.
q: It is divisble by 5.
(ii) p: A Natural number is odd.
q: Natyral number n is not divisible by 2.
(iii) p: A triangle is an equalateral triangle .
q: All the three sides of a triangle are equal.

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The correct Answer is:
To solve the problem, we need to convert the given biconditional statements into conditional statements. A biconditional statement of the form \( p \iff q \) can be expressed as two conditional statements: \( p \implies q \) and \( q \implies p \). Let's break down each part of the question step by step. ### (i) **Given:** - \( p \): The unit digit of an integer is zero. - \( q \): It is divisible by 5. **Biconditional Statement:** \( p \iff q \) **Step 1: Write the conditional statements.** 1. **If the unit digit of an integer is zero, then it is divisible by 5.** - This is \( p \implies q \). 2. **If it is divisible by 5, then the unit digit of an integer is zero.** - This is \( q \implies p \). **Final Conditional Statements:** - \( p \implies q \): If the unit digit of an integer is zero, then it is divisible by 5. - \( q \implies p \): If it is divisible by 5, then the unit digit of an integer is zero. ### (ii) **Given:** - \( p \): A natural number is odd. - \( q \): A natural number \( n \) is not divisible by 2. **Biconditional Statement:** \( p \iff q \) **Step 1: Write the conditional statements.** 1. **If a natural number is odd, then it is not divisible by 2.** - This is \( p \implies q \). 2. **If a natural number is not divisible by 2, then it is odd.** - This is \( q \implies p \). **Final Conditional Statements:** - \( p \implies q \): If a natural number is odd, then it is not divisible by 2. - \( q \implies p \): If a natural number is not divisible by 2, then it is odd. ### (iii) **Given:** - \( p \): A triangle is an equilateral triangle. - \( q \): All three sides of a triangle are equal. **Biconditional Statement:** \( p \iff q \) **Step 1: Write the conditional statements.** 1. **If a triangle is an equilateral triangle, then all three sides of the triangle are equal.** - This is \( p \implies q \). 2. **If all three sides of a triangle are equal, then it is an equilateral triangle.** - This is \( q \implies p \). **Final Conditional Statements:** - \( p \implies q \): If a triangle is an equilateral triangle, then all three sides of the triangle are equal. - \( q \implies p \): If all three sides of a triangle are equal, then it is an equilateral triangle. ### Summary of Conditional Statements: 1. **For (i)**: - \( p \implies q \): If the unit digit of an integer is zero, then it is divisible by 5. - \( q \implies p \): If it is divisible by 5, then the unit digit of an integer is zero. 2. **For (ii)**: - \( p \implies q \): If a natural number is odd, then it is not divisible by 2. - \( q \implies p \): If a natural number is not divisible by 2, then it is odd. 3. **For (iii)**: - \( p \implies q \): If a triangle is an equilateral triangle, then all three sides of the triangle are equal. - \( q \implies p \): If all three sides of a triangle are equal, then it is an equilateral triangle.

To solve the problem, we need to convert the given biconditional statements into conditional statements. A biconditional statement of the form \( p \iff q \) can be expressed as two conditional statements: \( p \implies q \) and \( q \implies p \). Let's break down each part of the question step by step. ### (i) **Given:** - \( p \): The unit digit of an integer is zero. - \( q \): It is divisible by 5. ...
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NCERT EXEMPLAR ENGLISH-MATHEMATICAL REASONING -OBJECTIVE TYPE QUESTIONS
  1. From the biconditional statement p harrq, where. (i) p: The un...

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  2. Which of the following is a statement ? x is a real no. switch off t...

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  3. Which of the following is not a statement.

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  5. The connective in the statement ''Earth revolves round the Sun and Mo...

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  7. The negative of the statement ''7 is greater than 8'' is

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  8. The negation of the statement ''72 is divisble by 2 and 3'' is

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  11. The negation of the statement ''101 is not mulitple of 3'' is

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  12. The contrapositive of the statement ''If 7 is greater than 5, then ...

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  13. The converse of the statement ''If x gt y, then x + a gt y + a'' is

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  14. The converse of the statement ''If sum is not shining, then sky is ...

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  15. The contrapositive of the statement If p then q is

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  16. The statement ''<b>If x^(2) is not even, then x is not even</b>'' is ...

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  17. The contrapositive of statement <b><b>'If Chandigarh is capital of P...

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  19. The negative of the statement ''The product of 3 and 4 is 9'' is

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  20. Which of the following is not a negative of ''A nature number is ...

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  21. Which of the following statement is a conjunction ?

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