Home
Class 12
MATHS
If a number is multiple of 5 then its en...

If a number is multiple of 5 then its end digit wiil be 5 or 0.
Contrarositive of above statement is

A

If a number is not multiple of 5, then it$ end digit will not be 5 or 0.

B

If end digit of a number is not 5 or 0 then it will not be multiple of 5.

C

If a number is not multiple of 5, then its end digit will be 5 or 0

D

If end digit of of number is 5 or 0, then the number will be 5.

Text Solution

AI Generated Solution

The correct Answer is:
To find the contrapositive of the given statement, we will follow these steps: 1. **Identify the original statement**: The original statement is "If a number is a multiple of 5, then its end digit will be 5 or 0." We can denote this as: - Let \( p \): "A number is a multiple of 5." - Let \( q \): "Its end digit will be 5 or 0." 2. **Write the contrapositive**: The contrapositive of a statement of the form "If \( p \), then \( q \)" is "If not \( q \), then not \( p \)". This can be expressed as: - If \( \neg q \), then \( \neg p \). 3. **Negate \( q \)**: The negation of \( q \) ("Its end digit will be 5 or 0") is: - \( \neg q \): "Its end digit will not be 5 or 0." 4. **Negate \( p \)**: The negation of \( p \) ("A number is a multiple of 5") is: - \( \neg p \): "It is not a multiple of 5." 5. **Combine the negations**: Now, we can combine these negations into the contrapositive statement: - "If its end digit is not 5 or 0, then it is not a multiple of 5." Thus, the contrapositive of the given statement is: **If its end digit is not 5 or 0, then it is not a multiple of 5.**
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION-B) (Objective type Questions (Only one answer))|10 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION-C) (Linked Comprehension Type Questions) (Comprehension-I)|3 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|18 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

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

Given two statements . P : 20 is a multiple of 5, q : 20 is a multiple of 7. Write the compound statement is 'P or q' and check its validity.

p : 87 is a multiple of 3 q : 87 is a multiple of 29 Write the compound statement by using connective "OR" from above statement and check its validity

Two statements are given : p: 30 is a multiple of 5. q: 30 is a multiple of 3. Conncet these two statements with word 'and' and check the validity of the compound statement.

Given below are two statement: p : 25 is a multiple of 5. q : 25 is a multiple of 8. Write the compound statement using connective "OR" and check its validity.

An eight digit number is a multiple of 73 and 137. If the second digit from left is 7, what is the 6th digit from the left of the number ?

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten's digit of the number are x and y respectively, then write the linear equation representing the above statement.

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5. and 7. what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?

Three-digit numbers are formed using the digits 0,1, 2, 3, 4, 5 without repetition of digits. If a number is chosen at random, then the probability that the digits either increase or decrease, is

Given below are two statements: p : 80 is a multiple of 5 q : 80 is a multiple of4. Write the compound statement using connective "AND" and check its validity.

AAKASH INSTITUTE ENGLISH-MATHEMATICAL REASONING-Assignment (SECTION-A) (Objective type Questions (Only one answer))
  1. "If p then q" is same as (where p and q are statement)

    Text Solution

    |

  2. p : If end digit of an integer is 5 then end digit of its square is al...

    Text Solution

    |

  3. If a number is multiple of 5 then its end digit wiil be 5 or 0. Cont...

    Text Solution

    |

  4. Contrapositive of "if p· then q" is (where p and q are statement)

    Text Solution

    |

  5. p : If an octagon in regular than all its side and angles are equal ...

    Text Solution

    |

  6. p : If a cylinder is right circular cylinder then its volume is 1/3pir...

    Text Solution

    |

  7. The converse of a given statement "if p, then q" is (where f and q are...

    Text Solution

    |

  8. p : · If nth term of a sequence is linear then sequence is in A.P. ...

    Text Solution

    |

  9. p : If a triangle is equilateral then its centroid, circumcenter and i...

    Text Solution

    |

  10. r : If a finite set has n elements then its total number of substets i...

    Text Solution

    |

  11. Equivalent form of " if and only if " for the given statements p and q...

    Text Solution

    |

  12. Equal chords of a circle are equidistant from the centre.

    Text Solution

    |

  13. r : Two chords of a circle subtend equal angles at centre if and only ...

    Text Solution

    |

  14. To check the validity of a statement p by contradiction method our ini...

    Text Solution

    |

  15. To check validity of statement we can use which of the following meth...

    Text Solution

    |

  16. p : sqrt(39) is irrational To check the validity of statement p , w...

    Text Solution

    |

  17. For the given statement identify the necessary condition p : If a fu...

    Text Solution

    |

  18. For the given statements identify the sufficient condition p·: If d...

    Text Solution

    |

  19. Negation of the given statement p is P : There exists a rational num...

    Text Solution

    |

  20. Converse of given statement p is, where P : If an event is sure eve...

    Text Solution

    |