class 11

Math

Algebra

Mathematical Reasoning

The statement $pqp $is equivalent to

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Find the component statements of the following compound statements and check whether they are true or false.(i) Number 3 is prime or it is odd.(ii) All integers are positive or negative.(iii) 100 is divisible by 3, 11 and 5.

Find out whether the following sentences is a statement or not. Justify your answer: the real number $x$ is less than 2.

Rewrite the following statement in the form $p$ if only if$q:$ If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.

Find the component statements of the following compound statement: 25 is a multiple of 5 and 8.

Are the following pairs of statements negations of each other:(i) The number x is not a rational number. The number x is not an irrational number.(ii) The number x is a rational number. The number x is an irrational number.

Rewrite each of the following statements in the form “p if and only if q(i) p: If you watch television, then your mind is free and if your mind is free, then you watch television.(ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.(iii) r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Determine the contrapositive of each of the following statements: (i)If Mohan is a poet, then he is poor. (ii)If she works, she will earn money. (iii)It never rains when it is cold.

Determine the contrapositive of each of the following statements: (i)Only if he does not tire will he win I(ii)f $x$ is an integer and $x_{2}$ is odd, then $x$ is odd (iii)Only if max studies will he pass the test.