Assume that an operation * is defined as follows: x * y = x' + y...

Assume that an operation * is defined as follows: x * y = x' + y Using Boolean algebra theorems and postulates (don’t use K-maps), check whether the operation * is associative or not?

Solutions

Expert Solution

the * operation is actually implication(->) operation and it is well known non associative operation. you can prove it using truth tables or just as follows:

the implication → is not associative. Compare (p→q)→r and p→(q→r). If p and r are true and q is false, then (p→q) is false, so (p→q)→r is true. But under the same conditions q→r is true, and therefore p→(q→r) is true. So (p→q)→r and p→(q→r) cannot be equivalent; that is, → is not associative.

venereology answered 1 year ago

Next > < Previous

Related Solutions

Let D(x, y) be the predicate defined on natural numbers x and y as follows: D(x,...

Let D(x, y) be the predicate defined on natural numbers x and y as follows: D(x, y) is true whenever y divides x, otherwise it is false. Additionally, D(x, 0) is false no matter what x is (since dividing by zero is a no-no!). Let P(x) be the predicate defined on natural numbers that is true if and only if x is a prime number. 1. Write P(x) as a predicate formula involving quantifiers, logical connectives, and the predicate D(x,...

Given a module which implements the function Z= F(X, Y), defined as follows: X +...

Given a module which implements the function Z= F(X, Y), defined as follows: X + Y when 10<=X<=20, and 12<=Y<=30 Z = X - Y when 0<=X<10, and 0<=Y<12 0 under other conditions where X and Y are integer parameters for F. 1. Identify the equivalence classes in [X, Y]. 2. List your test cases in [X, Y] based on your equivalence class analysis.

Assume a company produces two products: x and y. Assume the cost functions are as follows:...

Assume a company produces two products: x and y. Assume the cost functions are as follows: C(qx, 0) = 2qx^2 C(0, qy) = qy^2 C(qx, qy) = 2qx^2 + qy^2 + qxqy A. Calculate the economies of scale meaure (S) for x B. Does x exhibit economies of scale? C. Calculate the economies of scale meaure (S) for y D. Does y exhibit economies of scale? E. Calculate the economies of scope meaure (SC) F. Would it be better to...

Prove that The OR operation is closed for all x, y ∈ B x + y ∈ B

Boolean AlgebraProve that The OR operation is closed for all x, y ∈ B x + y ∈ BandProve that The And operation is closed for all x, y ∈ B x . y ∈ B

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...

An operation * is defined for two-valued variables a and b as follows: a*b = ab+a’b’

An operation * is defined for two-valued variables a and b as follows: a*b = ab+a’b’Let c = a*b. Determine which of the following identities are valid:a = b*ca*(bc) =1

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5]...

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5] (a) What is the value of the constant c? (b) Are X and Y independent? Explain. (c) What is the covariance oc X and Y? i.e. Cov(X ,Y)

The binormal distribution for (X, Y) is defined as the marginal distribution X ∼ N (1,4)...

The binormal distribution for (X, Y) is defined as the marginal distribution X ∼ N (1,4) and conditional distribution Y | X = x ∼ N (1 – x, 1). Find Pr(X < 1|Y = −1).

The value of f depends on two independent variables x and y as defined below: f(x,y)=x2+y2−x+3cos(x)sin(y)...

The value of f depends on two independent variables x and y as defined below: f(x,y)=x2+y2−x+3cos(x)sin(y) Function f has a minimum in the neighborhood of the origin (i.e. [0 0]). Find x and y which minimize f. Note: You are not allowed to use MATLAB built-in functions for optimization. Follow the logic of the derivative test: The minimum of f occurs where: ∂f∂x=0∂f∂y=0

Subjects