Chapter 2: Q27E (page 185)

Let $A = [\begin{array}{lll} 1 0 1 \\ 1 1 0 \\ 0 0 1 \end{array}] and B = [\begin{array}{lll} 0 1 1 \\ 1 0 1 \\ 1 0 1 \end{array}]$
Find
a) $A \lor B$ .
b) $A \land B$ .
c) $A ⊙ B$ .

Short Answer

Expert verified

a) Required answer is $A \lor B = [\begin{array}{lll} 1 1 1 \\ 1 1 1 \\ 1 0 1 \end{array}]$ .

b) Required answer is $A Λ B = [\begin{array}{lll} 0 0 1 \\ 1 0 0 \\ 0 0 1 \end{array}]$ .

c) Required answer is $A ⊙ B = [\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{matrix}]$

Step by step solution

Step 1:

Given: $A = [\begin{matrix} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] B = [\begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 0 & 1 \end{matrix}]$

(a) $A \lor B$ takes the disjunction of each element of B with the corresponding element of.

$A \lor B = [\begin{array}{ccc} 1 \lor 0 & 0 \lor 1 & 1 \lor 1 \\ 1 \lor 1 & 1 \lor 0 & 0 \lor 1 \\ 0 \lor 1 & 0 \lor 0 & 1 \lor 1 \end{array}]$

$b_{1} \lor b_{2}$ is equal to 1 if $b_{1} = 1$ or $b_{2} = 1$ (else 0 ).

role="math" localid="1668489394918" $A ν B = [\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{matrix}]$

Step 3:

(c) The ${(i j)}^{t h}$ element of the Boolean productrole="math" localid="1668489454199" $A ⊙ B$ takes the disjunction of all conjunctions of corresponding elements A and B in the ith row of A and in the jth column of.

role="math" localid="1668489606325" $\begin{aligned} A ⊙ B = [\begin{array}{lll} (1 \land 0) \lor (0 \land 1) \lor (1 \land 1) & (1 \land 1) \lor (0 \land 0) \lor (1 \land 0) & (1 \land 1) \lor (0 \land 1) \lor (1 \land 1) \\ (1 \land 0) \lor (1 \land 1) \lor (0 \land 1) & (1 \land 1) \lor (1 \land 0) \lor (0 \land 0) & (1 \land 1) \lor (1 \land 1) \lor (0 \land 1) \\ (0 \land 0) \lor (0 \land 1) \lor (1 \land 1) & (0 \land 1) \lor (0 \land 0) \lor (1 \land 0) & (0 \land 1) \lor (0 \land 1) \lor (1 \land 1) \end{array}] \end{aligned}$

$b_{1} \land b_{2}$ is equal to 1 if $b_{1} = b_{2} = 1$

$= [\begin{array}{lll} 0 \lor 0 \lor 1 1 \lor 0 \lor 0 1 \lor 0 \lor 1 \\ 0 \lor 1 \lor 0 1 \lor 0 \lor 0 1 \lor 1 \lor 0 \\ 0 \lor 0 \lor 1 0 \lor 0 \lor 0 0 \lor 0 \lor 1 \end{array}]$

$b_{1} \lor b_{2} \lor b_{3}$ is equal to 1 if $b_{1} = 1$ or $b_{2} = 1$ or $b_{3} = 1$

$= [\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{matrix}]$

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Let $A = [\begin{array}{lll} 1 0 1 \\ 1 1 0 \\ 0 0 1 \end{array}] and B = [\begin{array}{lll} 0 1 1 \\ 1 0 1 \\ 1 0 1 \end{array}]$
Find
a) $A \lor B$ .
b) $A \land B$ .
c) $A ⊙ B$ .

Short Answer

Step by step solution

Step 1:

Step 3:

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Let A=[1 0 11 1 00 0 1]andB=[0 1 11 0 11 0 1]Finda) A∨B.b) A∧B.c)A⊙B.

Short Answer

Step by step solution

Step 1:

Step 3:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Let $A = [\begin{array}{lll} 1 0 1 \\ 1 1 0 \\ 0 0 1 \end{array}] and B = [\begin{array}{lll} 0 1 1 \\ 1 0 1 \\ 1 0 1 \end{array}]$
Find
a) $A \lor B$ .
b) $A \land B$ .
c) $A ⊙ B$ .