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Q1. Write the hypothesis and the conclusion in the given implication. If one root of a quadratic equation is a + ib then the other root of the quadratic equation is a - ib.

Solution

Hypothesis: one root of a quadratic equation is a + ib Conclusion: the other root of the quadratic equation is a - ib. 

Q2. Write the connective used in the statementP: All whole numbers are either prime or composite.

Solution

The word 'Or' connects the two statements p: All whole numbers are prime, q: All whole numbers are composite, so the connective is 'Or'.

Q3. Find if the following sentences are statements or not(a) Life exists in planets other than the earth.(b) Give me your address

Solution

(a) The sentence is either true or false and thus it is a statement.(b) The sentence expresses a command which is neither true nor false and thus, it is not a statement.

Q4. Identify the quantifier in the given statement: P: There exists a whole number which is not natural. Write its truth value.

Solution

P: There exists a whole number which is not natural. Quantifier in the given statement is "There exists"Statement P is true since 0 is a whole number which is not natural.

Q5. Write the component statements of the given statement P: Number 7 is prime or it is odd.

Solution

The component statements arep: 7 is a prime number. q: 7 is odd 

Q6. Find the truth value of p : "Every real number is either prime or composite."

Solution

Giving one counter example is enough to prove the false hood of a statement. Here counter example is: The real number 1 is neither prime nor composite. So the statement is false. 

Q7. Given below is a pair of statements:Combine these two statements using "if and only if".p: If a rectangle is a square, then all its four sides are equal.q: If all the four sides of a rectangle are equal, then the rectangle is a square.

Solution

A rectangle is a square if and only if all its four sides are equal.

Q8. Write the contrapositive of the sentence: If I did not get the bus then I will drive.

Solution

Contrapositive of statement: If I did not drive then I got the bus (1 Mark)

Q9. Write the component statements of the following compound statement and check whether the compound statement is true or false.P: 0 is less than every positive integer and every negative integer'.

Solution

The component statements arep: 0 is less than every positive integer.q: 0 is less than every negative integer.The second statement is false.Therefore, the compound statement is false.

Q10. Write the contrapositive of the statement: 'If a number is divisible by 9, then it is divisible by 3'.

Solution

The contrapositive of the statements is:If a number is not divisible by 3, it is not divisible by 9.

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