is raining. q: It is cold. The connecting word is ‘and’. (iii)The component statements are p: All rational numbers are real.
q: All real numbers are complex. The connecting word is ‘and’. (iv)The component statements are MATHEMATICS p: is a positive number. q: is a negative number.
The connecting word is ‘or’. Example Find the component statements of the following and check whether they are true or not. A square is a quadrilateral and its four sides equal. All prime numbers are either even or odd.
(iii) A person who has taken Mathematics or Computer Science can go for MCA. (iv) Chandigarh is the capital of Haryana and UP. (v) is a rational number or an irrational number. (vi) is a multiple of , and .
Solution (i) The component statements are p: A square is a quadrilateral. q : A square has all its sides equal. We know that both these statements are true. Here the connecting word is ‘and’.
The component statements are p: All prime numbers are odd numbers. q: All prime numbers are even numbers. Both these statements are false and the connecting word is ‘or’. (iii) The component statements are p: A person who has taken Mathematics can go for MCA.
q: A person who has taken computer science can go for MCA. Both these statements are true. Here the connecting word is ‘or’. (iv) The component statements are p: Chandigarh is the capital of Haryana.
q: Chandigarh is the capital of UP. The first statement is true but the second is false. Here the connecting word is ‘and’. (v) The component statements are MATHEMATICAL REASONING p : is a rational number.
q : is an irrational number. The first statement is false and second is true. Here the connecting word is ‘or’. (vi) The component statements are p: is a multiple of .
q: is a multiple of . r: is a multiple of . All the three statements are true. Here the connecting words are ‘and’.
Thus, we observe