GATE CSE 2014 Set 1 | Question: 1

Question

Consider the statement

 "Not all that glitters is gold”

Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ is gold.  Which one of the following logical formulae represents the above statement?

• A. $\forall x: \text{glitters} (x)\Rightarrow \neg \text{gold}(x)$
• B. $\forall x:\text{gold} (x)\Rightarrow \text{glitters}(x)$
• C. $\exists x: \text{gold}(x)\wedge \neg \text{glitters}(x)$
• D. $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$

Comments

option B is not true because it says that " All gold glitters " which cannot be extracted from "Not all that glitters is gold"

we can only extract from this statement is "Some that glitters is not gold  "
We don't know about the gold that all of it glitters or not

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Understand the Difference between this & this.

If it says "None of that glitters is gold" then $\sim (\forall x(glitters(x)\rightarrow Gold(x)))$ will not work because this is saying some of that glitters is not gold (or) all of that glitters is not gold,  not None of that glitters is gold.

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Think domain as all the metals in the world.

Note :- glitter means “shines”

Understand meaning of each option in english below :-

Option A :- All the metals which glitter are not gold. (false because word “all” means gold are also included but gold always glitter)

Option B :- All the metals which are gold are glitter (although this statement is true but it not saying same thing as this statement “Not all that glitters is gold”)

Option C :- there exist a metal x which is gold but not glitter (this statement is always false)

Option D :- there exist a metal x which glitter but not gold (this is same statement that we have given in question)

So, option D is correct.

Answer 1

 

😊😊😊😊😊😊😊😊😊😊😊😊😊😊😊😊

Answer 2

The statement "Not all that glitters is gold" can be translated into logic as: "There exists something that glitters but is not gold."

Using the predicates defined above, this statement translates to:

∃x: glitters (x) ∧ ⇁ gold (x)

Therefore, the correct answer is option (D).