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Chapter 7: Problem 7

Using the boolean matrices $$ A=\left[\begin{array}{ll} 1 & 1 \\ 0 & 0 \end{array}\right], B=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right], \text { and } C=\left[\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right] $$ find each. $$A \odot(B \odot C)$$

Short Answer

Expert verified
Based on the given step-by-step solution, the short answer is: \(A \odot (B \odot C) = \left[\begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array}\right]\).

Step by step solution

01

Compute the boolean product of B and C.

The elementwise boolean product is computed entrywise: $$ B \odot C = \left[\begin{array}{cc} (0 \text{ AND } 0) & (1 \text{ AND } 0)\\\ (1 \text{ AND } 1) & (0 \text{ AND } 0) \end{array}\right] = \left[\begin{array}{cc} 0 & 0\\\ 1 & 0 \end{array}\right] $$
02

Compute the boolean product of A and (B猕�C)

Now, compute the elementwise boolean product of A and (B猕�C): $$ A \odot (B \odot C) = \left[\begin{array}{cc} (1 \text{ AND } 0) & (1 \text{ AND } 0)\\\ (0 \text{ AND } 1) & (0 \text{ AND } 0) \end{array}\right] = \left[\begin{array}{cc} 0 & 0\\\ 0 & 0 \end{array}\right] $$ Finally, we have computed the result of the elementwise boolean product A猕�(B猕�C): $$ A \odot (B \odot C) = \left[\begin{array}{cc} 0 & 0\\\ 0 & 0 \end{array}\right] $$

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