Home
Class 12
MATHS
If P, Q and R are the subsets of a set A...

If P, Q and R are the subsets of a set A, then prove that `Rxx(P^(c )uuQ^(c ))^(c )=(RxxP)nn(RxxQ)`.

Text Solution

AI Generated Solution

To prove the statement \( R \times (P^c \cup Q^c)^c = (R \times P) \cap (R \times Q) \), we will start by analyzing the left-hand side (LHS) and simplifying it step by step. ### Step 1: Start with the LHS The left-hand side is given as: \[ LHS = R \times (P^c \cup Q^c)^c \] ...
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos
  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos
  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos
  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If P is a proper subset of Q, then P nn Q =

For any sets A,B,C,D prove that: (A xx B)nn(C xx D)=(A nn C)xx(B nn D)

If P={a,b,c} and Q={r},form the set P times Q

Theorem 7 (For any set A;B;C;D prove that (A xx B)nn(C xx D)=(A nn C)xx(B nn D)

If A,B,C are three events associated with a random experiment prove that P(A uu B uu C)=P(A)+P(B)+P(C)-P(A nn C)-P(B nn C)+P(A nn B nn C)

If A;B and C are three events associated with a random experiments then P(A uu B uu C)=P(A)+P(B)+P(C)-P(A nn B)-P(B nn C)-P(C nn A

If P = {a, b, c} and Q = {r} , form the sets P xx Q and Q xx P .

If the p^(th), q^(th) and r^(th) terms of a H.P. are a,b,c respectively, then prove that (q - r)/(a) + (r - p)/(b) + (p - q)/(c) = 0