As mentioned in the text, the notation∃!xP(x) denotes "There exists a unique x such that P(x)is true." If the domain consists of all integers, what are the truth values of these statements? a) ∃!x(x > 1) b) ∃!x(x2 =1) c) ∃!x(x+3=2x) d) ∃!x(x = x +1)

Step-by-step explanation:

a)

If we take some random values like 5 and 10, it is clear that both 5 and 10 is greater than 1. Hence, there is no such unique x, for which P(x) > 1 is true. We can find multiple values which will be greater than 1.

b)

For both the values of x, 1 and -1, the value of is 1. In this case, we are getting at least two values of x, for which P(x) is true.

Hence, this statement is not true.

c)

.

In this scenario, we are getting an unique value of x that is 3, for which P(x) is true.

This statement is true.

d)

.

The above one is not an equation.

There is no meaning of the above.

Hence, this statement can not be true.

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol