adplus-dvertising
frame-decoration

Question

The notation ∃!xp(x) denotes the proposition "there exists a unique x such that P(x) is true".
Give the truth values of the following statements :

I. ∃!xP(x) → ∃xP(x)
II. ∃!x ¬ P(x) → ¬∀xp(x)

a.

Both I and II are true

b.

Both I and II are false

c.

I-false, II-true

d.

I-true, II-false

Answer: (a).Both I and II are true

Engage with the Community - Add Your Comment

Confused About the Answer? Ask for Details Here.

Know the Explanation? Add it Here.

Q. The notation ∃!xp(x) denotes the proposition "there exists a unique x such that P(x) is true". Give the truth values of the following statements : I. ∃!xP(x) → ∃xP(x) II. ∃!x...

Similar Questions

Discover Related MCQs

Q. Give a compound proposition involving propositions p, q and r that is true when exactly two of p, q and r are true and is false otherwise.

Q. The quantification ∃!x P(x) denotes the proposition “There exists a unique x such that P(x) is true”, express the quantification using universal and existential quantifications and logical operators:

Q. Which of the following is a correct predicate logic statement for “Every Natural number has one successor” ?

Q. α – β cutoffs are applied to .............

Q. Assume that each alphabet can have a value between 0 to 9 in a cryptoarithmetic problem 
   CROSS+ROADS
--------------
DANGER
--------------
Which of the following statement is true ?

(i) No two alphabets can have the same numeric value.
(ii) Any two alphabets may have the same numeric value.
(iii) D = 0
(iv) D = 1

Q. Which of the following is not a part of an expert system shell ?

Q. The Blocks World Problem in Artificial Intelligence is normally discussed to explain a ..................

Q. Means-Ends Analysis process centres around the detection of difference between the current state and the goal state. Once such a difference is found, then to reduce the difference one applies ..................

Q. If an artificial variable is present in the ‘basic variable’ of optimal simplex table then the solution is .................

Q. An optimal assignment requires that the minimum number of horizontal and vertical lines that can be drawn to cover all zeros be equal to the number of

Q. The tracing model in Prolog describes program execution in terms of certain events. These events are

Q. Which of the following shall be a compound proposition involving the propositions p, q and r, that is true when exactly two of the p, q and r are true and is false otherwise?

Q. The truth value of the statements:

∃!xP(x)→∃xP(x) and ∃!x˥P(x)→˥∀xP(x), (where the notation ∃!xP(x) denotes the proposition "There exists a unique x such that P(x) is true'') are:

Q. Horn clauses are special kinds of propositions which can be described as

Q. Which of the following is/are the fundamental semantic model(s) of parameter passing?

Q. Which one of the following is a correct implementation of the metapredicate “not” in PROLOG (Here G represents a goal) ?

Q. Which one of the following is not an informed search technique?

Q. If we convert

∃u ∀v ∀x ∃y (P(f(u),v, x, y) → Q(u,v,y)) to
∀v ∀x (P(f(a),v, x, g(v,x)) → Q(a,v,g(v,x)))

This process is known as

Q. Given two jugs of capacities 5 litres and 3 litres with no measuring markers on them. Assume that there is endless supply of water. Then the minimum number of states to measure 4 litres water will be

Q. The map colouring problem can be solved using which of the following technique?