write each of the following using ‘if and only if’ : (i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly. (ii) If you watch television, then your mind is free, and if your mind is free, then you watch television.

Home » write each of the following using ‘if and only if’ : (i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly. (ii) If you watch television, then your mind is free, and if your mind is free, then you watch television.

write each of the following using ‘if and only if’ :
(i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly.
(ii) If you watch television, then your mind is free, and if your mind is free, then you watch television.

RS Agarwal Maths Class 11 Mathematical Reasoning

write each of the following using ‘if and only if’ :
(i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly.
(ii) If you watch television, then your mind is free, and if your mind is free, then you watch television.

(i) You get an A grade if and only if you do all your homework regularly.
(ii) You watch television if and only if your mind is free.

i

By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

Use contradiction method to prove that :

By giving a counter-example, show that the statement is false :
p : If n is an odd positive integer, then n is prime.

Consider the statement :
q : For any real numbers a and b, a2 = b2⇒ a = b
By giving a counter-example, prove that q is false.

Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.

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By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

Use contradiction method to prove that :

By giving a counter-example, show that the statement is false :
p : If n is an odd positive integer, then n is prime.

Consider the statement :
q : For any real numbers a and b, a2 = b2⇒ a = b
By giving a counter-example, prove that q is false.

Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.

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