Mathematical Reasoning — Maths STD 11 Science — Question

Which of the following statements are true and which are false? In each case give a valid reason for saying so:
r: Circle is a particular case of an ellipse.

If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A - C) × (B - C).

Write the solution set of the inequation |2 - x| = x - 2.

Which of the following statements are true and which are false? In each case give a valid reason for saying so:
p: Each radius of a circle is a chord of the circle.

Find the component statements of the following compound statements.
The number 100 is divisible by 3, 11 and 5.

Write down the converse of following statement:
If all three angles of a triangle are equal, then the triangle is equilateral.

Rewrite the following statements in the form "p if and only if q".
p: If you watch television, then your mind is free and if your mind is free, then you watch television.

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
There exists real numbers x and y for which x + y = y + x.

Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.