Translate the following statements into symbolic form:

i. Rahul passed in Hindi and English.

ii. x and y are even integers.

iii. 2, 3, and 6 are factors of 12.

iv. Either x or x + 1 is an odd integer.

v. A number is either divisible by 2 or 3.

vi. Either x = 2 or x = 3 is a root of 3x² – x – 10 = 0.

vii. Students can take Hindi or English as an optional paper.

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Payal Gupta | Contributor-Level 10

7 months ago

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l} (i) p : R a h u l p a s s e d i n H i n d i . \\ q : R a h u l p a s s e d i n E n g l i s h . \\ p \land q : R a h u l p a s s e d i n H i n d i a n d E n g l i s h . \\ (i i) p : x i s a n e v e n i n t e g e r . \\ q : y i s a n e v e n i n t e g e r . \\ p \land q : x a n d y a r e e v e n i n t e g e r . \\ (i i i) p : 2 i s a f a c t o r o f 12 . \\ q : 3 i s a f a c t o r o f 12 . \\ r : 6 i s a f a c t o r o f 12 . \\ p \land q \land r : 2, 3 a n d 6 a r e f a c t o r s o f 12 . \\ (i v) p : x i s a n o d d i n t e g e r . \\ q : x + 1 i s a n o d d i n t e g e r . \\ p \lor q : E i t h e r x o r x + 1 i s a n o d d i n t e g e r . \\ (v) p : A n u m b e r i s d i v i s i b l e b y 2 . \\ q : A n u m b e r i s d i v i s i b l e b y 3 . \\ p \lor q : A n u m b e r i s d i v i s i b l e b y 2 o r 3 . \\ (v i) p : x = 2 i s a r o o t o f t h e e q u a t i o n 3 x^{2} - x - 10 = 0 . \\ q : x = 3 i s a r o o t o f t h e e q u a t i o n 3 x^{2} - x - 10 = 0 . \\ p \lor q : E i t h e r x = 2 o r x = 3 i s t h e r o o t o f t h e e q u a t i o n 3 x^{2} - x - 10 = 0 . \\ (v i i) p : H i n d i i s t h e o p t i o n a l p a p e r . \\ q : E n g l i s h i s t h e o p t i o n a l p a p e r . \\ p \lor q : E i t h e r H i n d i o r E n g l i s h i s o p t i o n a l p a p e r . \end{array}$