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Standard XII

Mathematics

Method of Contradiction

a, b, c are p...

Question

$a, b, c$ are prime numbers, $x$ is an even number, $y$ is an odd number. Which of the following is/are never true?
$I .$ $a + x = b$
$I I .$ $b + y = c$
$I I I .$ $a b = c$
$I V .$ $a + b = c$

I

and

I I

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I I

and

I I I

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Only

I I I

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I I I

and

I V

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Solution

The correct option is B Only $I I I$
Multiplication of 2 prime number is not a prime number. Whereas the other identities are true.

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Similar questions

If A = {x: x is a natural number}, B ={x: x is an even natural number}

C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

(i) A ∩ B

(ii) A ∩ C

(iii) A ∩ D

(iv) B ∩ C

(v) B ∩ D

(vi) C ∩ D

Q. If

A = {x : x

is a natural number

}, B = {x : x

is an even natural number

} C = {x : x

is an odd natural number

}

and

D = {x : x

is a prime number

},

find
(i)

A \cap B

(ii)

A \cap C

(iii)

A \cap D

(iv)

B \cap C

(v)

B \cap D

(vi)

C \cap D

Q. Some persons and events are stated below :
Which ofthe following match correctly
(1) A- III B- I C- IV D- II
(2) A- I B- III C -IV D- II
(3) A -III B- IV C- I D -II
(4) A- II B -IV C -I D -III

Match the following:

$\begin{matrix} P o i n t & I n v a r i a n t w i t h r e s p e c t t o l i n e a . & (- 3, 2) & (i) & y = 4 b . & (2, - 3) & (i i) & x = 4 c . & (- 1, 4) & (i i i) & y = 2 d . & (4, - 1) & (i v) & x = 2 \end{matrix}$

Match the following vitamins and minerals with their sources. $\begin{matrix} Column-I & Column - II (i) & Amla & (a) & Calcium (ii) & Carrot & (b) & Iodine (iii) & Milk & (c) & Vitamin C (iv) & Salt & (d) & Vitamin A \end{matrix}$

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a,b,c are prime numbers, x is an even number, y is an odd number. Which of the following is/are never true?I. a+x=bII. b+y=cIII. ab=cIV. a+b=c

The correct option is B Only IIIMultiplication of 2 prime number is not a prime number. Whereas the other identities are true.

$a, b, c$ are prime numbers, $x$ is an even number, $y$ is an odd number. Which of the following is/are never true?
$I .$ $a + x = b$
$I I .$ $b + y = c$
$I I I .$ $a b = c$
$I V .$ $a + b = c$

The correct option is B Only $I I I$
Multiplication of 2 prime number is not a prime number. Whereas the other identities are true.