Write the component statements of the following compound statements and check whether the compound statement is true or false:

i. 57 is divisible by 2 or 3.

ii. 24 is a multiple of 4 and 6.

iii. All living things have two eyes and two legs.

iv. 2 is an even number and a prime number.

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Payal Gupta | Contributor-Level 10

7 months ago

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

$\begin{array}{l} (i) H e r e t h e g i v e n s t a t e m e n t i s t h e f o r m p \lor q w h i c h h a s t h e t r u t h v a l u e T w h e n e v e r e i t h e r \\ p o r q b o t h h a v e t h e t r u t h v a l u e T . \\ H e n c e, I t i s a t r u e s t a t e m e n t a n d i t s c o m p o n e n t s t a t e m e n t s a r e \\ p : 57 i s d i v i s i b l e b y 2 . (F a l s e) \\ q : 57 i s d i v i s i b l e b y 3 . (T r u e) \\ (i i) H e r e t h e g i v e n s t a t e m e n t i s t h e f o r m p \land q w h i c h h a s t h e t r u t h v a l u e T w h e n e v e r b o t h \\ p o r q h a v e t h e t r u t h v a l u e T . \\ H e n c e, I t i s a t r u e s t a t e m e n t a n d i t s c o m p o n e n t s t a t e m e n t s a r e \\ p : 24 i s a m u l t i p l e o f 4 . (T r u e) \\ q : 24 i s a m u l t i p l e o f 6 . (T r u e) \\ (i i i) I t i s a f a l s e s t a t e m e n t . S ince p \land q w h i c h h a s t h e t r u t h v a l u e F w h e n e v e r e i t h e r \\ p o r q o r b o t h h a v e t h e t r u t h v a l u e F . I t s c o m p o n e n t s t a t e m e n t s a r e \\ p : A l l l i v i n g t h i n g s h a v e t w o e y e s . (F a l s e) \\ q : A l l l i v i n g t h i n g s &thins \end{array}$