Home
Class 12
MATHS
Prove (A cap B)'=(A' cup B')...

Prove `(A cap B)'=(A' cup B')`

Text Solution

Verified by Experts

For all `x in (A cap B)`
`Leftrightarrow x in (A cap B)`
`Leftrightarrow x notin (A cap B)`
`Leftrightarrow x notin A or x notin B`
`Leftrightarrow x in A' or x in B`
`Leftrightarrow x in A' cup B`
Hence, `(A cap B)'=A' cup B`
Promotional Banner

Topper's Solved these Questions

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-A(Objective Type Questions (One option is correct))|41 Videos

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-B(Objective Type Question(One option is correct))|13 Videos

  • SETS

    AAKASH INSTITUTE|Exercise EXAMPLE|24 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 Videos

  • STATISTICS

    AAKASH INSTITUTE|Exercise Section-C Assertion-Reason|15 Videos

Similar Questions

Explore conceptually related problems

Prove A cup (B cap C)=(A cup B) cap(A cup C)

Prove that A cap (A cup B)'=phi .

If A and B are two sets, then (A cup B')' cap (A' cup B)' is

Draw the Venn diagram for each of the following : (i) (A cap B)' (ii) (A cup B)' (iii) A' cup B' (iv) A' cap B' .

Two sets A and B are such that n(A cup B)=21,n(A' cap B')=9,n(A cap B)=7 find n(A cap B)'

Prove the distributive law and De Morgan's law. (i) A cap (B cup C)=(A cap B)cup(A cap C) (ii) (A cup B)'=A' cap B'

Consider the following 1. A cup (B cap C) = (A cap B) cup (A cap C) II. A cap (B cup C) = (A cup B) cap (A cup C) Which of the above statement(s) is/are correct?

Using properties of sets and their complements prove that (i) (A cup B)cap (A cup B') = A

Suppose A, B and C are three sets. Consider the following: (i) A cup (B cap C) = (A cup B) cap (A cup C) (ii) (A cap B) cup C = (A cup C) cap (B cup C) Which of the above is true?

AAKASH INSTITUTE-SETS -Try yourself
  1. Write down the complement of given set A (i) A={x,x in N}, set of wh...

    Text Solution

    |

  2. Write down the complement of given set A (i) N is universal set, A={...

    Text Solution

    |

  3. If universal set U={1,2,3,4,5,6,7,8,9}, A={1,5,6},B={4,8,9},C={3,2,6} ...

    Text Solution

    |

  4. If universal set, U={x:x is a letter in the phrase The MAD DONKEY} A...

    Text Solution

    |

  5. Draw the venn diagram to represent (i) A cap (B-A)' & (ii) A cup B(B...

    Text Solution

    |

  6. If U={1,2,3……10}, A={1,5,6}, B={3,4,5}, C={6,5,3,10}, then represent t...

    Text Solution

    |

  7. Prove A cup (B cap C)=(A cup B) cap(A cup C)

    Text Solution

    |

  8. Prove (A cap B)'=(A' cup B')

    Text Solution

    |

  9. If X and Y are two sets such that X cup Y has 50 elements, X has 24 el...

    Text Solution

    |

  10. If A and B are two sets such that A cup B has 64 elements, A has 40 el...

    Text Solution

    |

  11. If A and B are two sets such that n(A)=30, n(B)=26 and n(A cup B)=50,...

    Text Solution

    |

  12. If A and B are two sets such that n(A)=24, n(B)=13 and n(A cup B) =32 ...

    Text Solution

    |

  13. If n(U)=60, n(A)=26 and n(B)=36 where U is the universal set then find...

    Text Solution

    |

  14. If n(U)=1200, n(A)=900 and n(B)=700 where U is the universal set then ...

    Text Solution

    |

  15. In a class of 30 students, 13 like to eat cake and 26 like to eat ice ...

    Text Solution

    |

  16. In a class of 195 students, 115 like football, 130 like basket ball. I...

    Text Solution

    |

  17. In a group of students, there are 24 opting for photography and 26 opt...

    Text Solution

    |

  18. In an adventure trip, there are 50 people interested for camel riding ...

    Text Solution

    |

  19. In an university, out of 100 students, 16 opted mathematics only, 24 o...

    Text Solution

    |

  20. In a group of 200 students, 20 played cricket only, 36 plated tennis o...

    Text Solution

    |