Home
Class 12
MATHS
Given below are two pairs of statement ....

Given below are two pairs of statement . Combine these two statement using " if and only if "
(i) p : If a rhombus is a square , then all its angles are `90^@`
q : If all the angles of a rhombus are `90^@` , then it is sqaure
(ii) p : If the sum of digit of a number is divisble by 9 , then the number is divisble by 9
q : If a number is divisble by 9 , then the sum of its digit is divisble by 9

Text Solution

AI Generated Solution

To combine the given pairs of statements using "if and only if," we can follow these steps: ### Step 1: Understand the Statements We have two pairs of statements: 1. **Pair 1:** - Statement P: If a rhombus is a square, then all its angles are \(90^\circ\). - Statement Q: If all the angles of a rhombus are \(90^\circ\), then it is a square. ...
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|18 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION-A) (Objective type Questions (Only one answer))|50 Videos
  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Section - j|3 Videos
  • MATRICES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - J) Aakash Challengers Questions|3 Videos

Similar Questions

Explore conceptually related problems

Given below are two pairs of statements. Combine these two statements using if and only if.(i) p: If a rectangle is a square, then all its four sides are equal. q: If all the four sides of a rectangle are equal, then the rectangle is a square.(ii) p: If the sum of digits of a number is divisible by 3, then the number is divisible by 3. q: If a number is divisible by 3, then the sum of its digits is divisible by 3.

Given below are two pairs of statements. Combine these two statements using "if and only if". (i) p: If a rectangle is a square, then all its four sides are equal. q: If all the four sides of a rectangle are equal, then the rectangle is a square.

Given below are two pairs of statements. Combine these two statements using if and only if: p : if a rectangle is a square, then all its four sides are equal. q : if all the four sides of a rectangle are equal, then the rectangle is a square

Given below are two pairs of statements. Combine these two statements using if and only if: p : if the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q : if a number is divisible by 3, then the sum of its divisible by 3.

Given below are two pairs of statement , combine these two statement using "if and only if" (i) p : If a polygon is convex then all its diagonal lies inside the polygon q : If all the diagonals of a polygon lie inside if then it is convex (ii) p : If a physical quantity has magnitude only then it is scalar q : If a physical quantity is scalar , then it has magnitude only

Write the following statement in conditional form. Every rhombus is a square.

One of the diagonals of a rhombus is equal to one of its sides. Find the angles of the rhombus.

If the longer diagonal of a rhombus is 10 and the large angle is 100^(@) , what is the area of the rhombus ?

Statement-1 : A natural number is chosen at random. The probability that the sum of the squares of its digits is 93, is 0. Statement-2 : A number is divisble by 31 iff sum of its digits is divisible by 31.

Write the contrapositive of the following statement (i) If a quandrilateral is rectangle then it is a parallelogram (ii) If a number is even , then it is divisble by 2 (iii) If end digit of a number is 0 , then it is divisble by 10

AAKASH INSTITUTE ENGLISH-MATHEMATICAL REASONING-Assignment (SECTION-D) (Assertion-Reason Type Questions)
  1. Given below are two pairs of statement . Combine these two statement u...

    Text Solution

    |

  2. Let p be the statement "It rains"! and q be the statement "It is cold"...

    Text Solution

    |

  3. If p, q, r be anY three. statements STATEMENT-1 : pvv(q^^r)hArr(pvvq...

    Text Solution

    |

  4. STATEMENT-1 : The converse of p rArr q " is " q rArr p and STAT...

    Text Solution

    |

  5. STATEMENT-1 : ~(prArrq)=p^^~q and STATEMENT-2 : p rArr q = ~p ...

    Text Solution

    |

  6. STATEMENT-1 : (phArrq)=~ p hArr q and STATEMENT-2 : (phArrq) ...

    Text Solution

    |

  7. Let p be the statement "x is divisible b, 4" and q be the statement "x...

    Text Solution

    |

  8. STATEMENT-1 : The inverse of (p^^~q) rArrr " is "~pvvqrArr ~r and ...

    Text Solution

    |

  9. STATEMENT-1 : If (p^^~r)rArr(qvvr) is false and q and r are false , th...

    Text Solution

    |

  10. STATEMENT-1 : p hArr ~q is true, when pis false and q is true. and ...

    Text Solution

    |

  11. STATEMENT-1 : (p^^~q)^^(~p^^q) and STATEMENT-2 : (pvv~q) vv (~p...

    Text Solution

    |

  12. STATEMENT-1 : (p rArr q) hArr (~q rArr~p) and STATEMENT-2 : p rA...

    Text Solution

    |

  13. STATEMENT-1 : (p rArr ~q) ^^ (~q rArr q) is a contradication and ...

    Text Solution

    |

  14. STATEMENT-1 : The dual statement of "xis a perfect square or xis a pri...

    Text Solution

    |

  15. STATEMENT-1 : [p^^(pvvq)]vv[q^^(qvvp)]=pvvq and STATEMENT-2 : p...

    Text Solution

    |

  16. STATEMENT-1 : ~(phArrq)=~phArrq=phArr~q and STATEMENT-2 : (phArr...

    Text Solution

    |