English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

Let A = (101001011001), B = (010110101001), C = (110101101111) be any three boolean matrices of the same type. Find (A ∧ B) v C - Mathematics

Advertisements
Advertisements

Question

Let A = `((1, 0, 1, 0),(0, 1, 0, 1),(1, 0, 0, 1))`, B = `((0, 1, 0, 1),(1, 0, 1, 0),(1, 0, 0, 1))`, C = `((1, 1, 0, 1),(0, 1, 1, 0),(1, 1, 1, 1))` be any three boolean matrices of the same type. Find (A ∧ B) v C

Sum

Solution

Given boolean matrices

A = `((1, 0, 1, 0),(0, 1, 0, 1),(1, 0, 0, 1))`

B = `((0, 1, 0, 1),(1, 0, 1, 0),(1, 0, 0, 1))`

C = `((1, 1, 0, 1),(0, 1, 1, 0),(1, 1, 1, 1))`

(A ∧ B) v C = `((0, 0, 0, 0),(0, 0, 0, 0),(1, 0, 0,  1)) vv ((1, 1, 1, 1),(0, 1, 1, 0),(1, 1, 1, 1))`

= `((0 vv 1, 0 vv 1, 0 vv 0, 0 vv 1),(0 vv 0, 0 vv 1, 0 vv 1, 0 vv 0),(1 vv 1, 0 vv 1, 0 vv 1, 1 vv 1))`

= `((1, 1, 0, 1),(0, 1, 1, 0),(1, 1, 1, 1))`

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Discrete Mathematics - Exercise 12.1 [Page 236]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 12 Discrete Mathematics
Exercise 12.1 | Q 8. (iv) | Page 236

RELATED QUESTIONS

Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this.

On Z+, define * by a


For each binary operation * defined below, determine whether * is commutative or associative.

On Z, define − b


Determine whether the following operation define a binary operation on the given set or not : '*' on N defined by a * b = a + b - 2 for all a, b ∈ N


Let * be a binary operation on the set I of integers, defined by a * b = 2a + b − 3. Find the value of 3 * 4.


Prove that the operation * on the set

\[M = \left\{ \begin{bmatrix}a & 0 \\ 0 & b\end{bmatrix}; a, b \in R - \left\{ 0 \right\} \right\}\] defined by A * B = AB is a binary operation.


Let * be a binary operation on N given by a * b = LCM (a, b) for all a, b ∈ N. Find 5 * 7.


Check the commutativity and associativity of the following binary operations '*'. on N defined by a * b = 2ab for all a, b ∈ N ?


Check the commutativity and associativity of the following binary operations '⊙' on Q defined by a ⊙ b = a2 + b2 for all a, b ∈ Q ?


Let * be a binary operation on Z defined by
a * b = a + b − 4 for all a, b ∈ Z Show that '*' is both commutative and associative ?


Let * be the binary operation on N defined by a * b = HCF of a and b.
Does there exist identity for this binary operation one N ?


Let A  \[=\] R  \[\times\] R and \[*\]  be a binary operation on defined by \[(a, b) * (c, d) = (a + c, b + d) .\] . Show that \[*\] is commutative and associative. Find the binary element for \[*\] on A, if any.


For the binary operation ×7 on the set S = {1, 2, 3, 4, 5, 6}, compute 3−1 ×7 4.


Find the inverse of 5 under multiplication modulo 11 on Z11.


Write the composition table for the binary operation multiplication modulo 10 (×10) on the set S = {2, 4, 6, 8}.


If the binary operation * on Z is defined by a * b = a2 − b2 + ab + 4, then value of (2 * 3) * 4 is ____________ .


If the binary operation ⊙ is defined on the set Q+ of all positive rational numbers by \[a \odot b = \frac{ab}{4} . \text{ Then }, 3 \odot \left( \frac{1}{5} \odot \frac{1}{2} \right)\] is equal to __________ .


The binary operation * defined on N by a * b = a + b + ab for all a, b N is ________________ .


Define an operation * on Q as follows: a * b = `(("a" + "b")/2)`; a, b ∈ Q. Examine the closure, commutative and associate properties satisfied by * on Q.


A binary operation on a set has always the identity element.


Which of the following is not a binary operation on the indicated set?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×