class 11

Math

Algebra

Mathematical Reasoning

The statement $(p↔q)$ is

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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.

Which of the following statements are true and which are false? In each case give a valid reason for saying so(i) p : Each radius of a circle is a chord of the circle(ii) q : The centre of a circle bisects each chord of the circle(iii) r : Circle is a particular case of an ellipse(iv) s : If x and y are integers such that $x>y$ then $−x<−y$(v) t : $11 $ is a rational number

Write the negation of the following statements:(i) Chennai is the capital of Tamil Nadu(ii) $2 $ is not a complex number (iii) All triangles are not equilateral triangle(iv) The number $2$ is greater than $7$(v) Every natural number is an integer

Find the component statements of the following compound statement: It is raining and it is cold.

Rewrite the following statement with if then in five different ways conveying the same meaning: If a natural number is odd, then its square is also odd.

Are the following pairs of statements are negation of each other: The number $x$ is not a rational number. The number $x$ is an irrational number.

Identify the quantifier in each of the following statements: (i)For every real number $x,x+4$ is greater then $x˙$ (ii)There exists a real number which is twice of itself. (iii)There exists a (living) person who is 200 years old. (iv)For every $x∈N,x+1>x˙$

Write the negation of the following statements: (i)All students live in the dormitories (ii)Some students are 25 (years) or older.