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Write down the converse of the following statements:

i. If a rectangle R is a square, then R is a rhombus.

ii. If today is Monday, then tomorrow is Tuesday.

iii. If you go to Agra, then you must visit the Taj Mahal.

iv. If the sum of squares of two sides of a triangle is equal to the square of the third side of the triangle, then the triangle is right-angled.

v. If all three angles of a triangle are equal, then the triangle is equilateral.

vi. If x:y=3:2 , then 2x=3y .

vii. If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.

viii. If x is zero, then x is neither positive nor negative.

ix. If two triangles are similar, then the ratio of their corresponding sides is equal.

0 2 Views | Posted 3 months ago
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  • 1 Answer

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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

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

    ( i ) I f     t h e     r e c t a n g l e     R       i s     r h o m b u s ,     t h e n     i t     i s     a     s q u a r e . ( i i ) I f     t o m o r r o w     i s     T u e s d a y ,     t h e n     t o d a y     i s     M o n d a y . ( i i i ) I f     y o u     m u s t     v i s i t     t h e     T a j     M a h a l ,     t h e n     y o u     g o     t o     A g r a . ( i v )   I f     t h e     t r i a n g l e     i s     r i g h t     t r i a n g l e ,     t h e n     t h e     s u m     o f     t h e     s q u a r e s     o f     t w o     s i d e s     o f     a     t r i a n g l e         is  equal  to  the  square  of  the  third  side  of  the  triangle. ( v ) I f     t h e     t r i a n g l e     i s     e q u i l a t e r a l ,     t h e n     a l l     t h r e e     a n g l e s     o f     a     t r i a n g l e     a r e     e q u a l . ( v i ) I f     2 x = 3 y     t h e n     x : y = 3 : 2 . ( v i i ) I f     t h e     o p p o s i t e     a n g l e s     o f     a     q u a d r i l a t e r a l     a r e     s u p p l e m e n t a r y ,     t h e n     S     i s     c y c l i c . ( v i i i ) I f     x     i s       n e i t h e r     p o s i t i v e     n o r     n e g a t i v e     t h e n     x = 0 . ( i x )     I f     t h e     r a t i o     o f     c o r r e s p o n d i n g     s i d e s     o f     t w o     t r i a n g l e s     a r e     e q u a l ,     t h e n     t r i a n g l e s     a r e     s i m i l a r .

Similar Questions for you

Let Δ , ∇ ∈ { ∧ , ∨ } be such that p ∇ q ⇒ ( ( p Δ q ) ∇ r ) is a tautology. Then ( p ∇ q ) Δ   r  is logically equivalent to:
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Raj Pandey

Case – I Δ ≡ ∇ ≡ ∧  

              ( p ∧ q ) → ( ( p ∧ q ) ∧ r )  

              it can be false if r is false,

              so not a tautology

              Case – II If Δ ≡ ∇ ≡ ∨  

              ( p ∨ q ) ?     → ( ( p ∨ q ) ∨ r ) ≡ tautology

              then ( p ∨ q ) ∨ r ≡ ( p Δ r ) ∨ q   

              Case – I

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Negation of the Boolean statement ( p ∨ q ) ⇒ ( ( ∼ r ) ∨ p )  is equivalent to
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Vishal Baghel

pva ( ∼ r   v   p )

∼ ( p ∨ q ) ∨ ( ∼ r v p )

its negation as asked in question

( p ∨ q ) ∧ ( ∼ p ∧ r )

= ( p ∧ ∼ p ∧ r ) ∨ ( q ∧ r ∧ ∼ p )

= ( p ∧ r ∧ ∼ p )                   [ a s     p ∧ ∼ p     i s     f a l s e ]

The remainder when (2021)2023 is divided by 7 is:
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Raj Pandey

2 0 2 1 ≡ − 2 mod (7)

⇒ ( 2 0 2 1 ) 2 0 2 3 ≡ ( − 2 ) 2 0 2 3 m o d ( 7 )   …… (i)

Now,   ( − 2 ) 3 ≡ − 1 m o d ( 7 )  

⇒ ( − 2 ) 2 0 2 3 ≡ ( − 2 ) m o d ( 7 ) ≡ 5 m o d ( 7 )       ……. (ii)

(i) & (ii)

⇒ ( 2 0 2 1 ) 2 0 2 3 ≡ 5 m o d ( 7 )  

∴  Remainder = 5

Let p, q, r be three logical statements. Consider the compound statements

  S 1 : ( ( ∼ p ) ∨ q ) ∨ ( ( ∼ p ) ∨ r )     a n d  

  S 2 : p → ( q ∨ r )  

 Then, which of the following is NOT true?
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Raj Pandey

kindly consider the following Image 

 

The statement ( ∼ ( p ⇔ ∼ q ) ) ∧ q     i s :  
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Raj Pandey

∼ ( p ⇔ ∼ q ) ∧ q = ( p ⇔ ∼ q ) ∧ q     i s :

∴ ( ∼ ( P ⇔ ∼ Q ) ) ∧ q is equivalent to ( p ⇒ q ) ∧

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