TIFR CSE 2014 | Part A | Question: 8

Question

All that glitters is gold. No gold is silver.

Claims:

1. No silver glitters.
2. Some gold glitters.

Then, which of the following is TRUE?

• A. Only claim $1$ follows.
• B. Only claim $2$ follows.
• C. Either claim $1$ or claim $2$ follows but not both.
• D. Neither claim $1$ nor claim $2$ follows.
• E. Both claim $1$ and claim $2$ follow.

Answer 1

The correct answer is option (a) Only claim 1 follows.

$\text{Glitters}(x) \implies \text{ Gold}(x) \implies \lnot \text{ Silver}(x)$. Hence, Claim 1 follows. If something Glitters, it cannot be Silver.

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For claim 2:

The set of things that Glitter could be empty.

We can still assert that All that Glitters is Gold, because nothing Glitters in the first place.

So, in the case when nothing Glitters, there is no Gold that Glitters. Glitters is still a subset of Gold, but there is no element in the subset Glitters.

Comments

You are correct. good approach

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ans would be e both the conclusion follow here.

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Can you explain why "Some gold may glitter" will be true? and how is it any different than “some gold glitters”? Because both the cases imply a “possibility ”. Some gold may glitter. There is a possibility of some gold which glitters. Some gold glitter; there is a possibility that there exists a piece of gold that glitters. 

 

Answer 2

$$\require{enclose}\enclose{circle}{\matrix{\\\rm is~Gold\\\enclose{circle}{\matrix{\\\rm Glitters\\\,}}\\\,}}\quad\enclose{circle}{\matrix{\\\rm Silver\\\,}}$$

Ans will be (e)

glitter is subset of gold, So some gold glitter and some not glitter, So (2) follows

silver is totally other set, because when something glitters, it must be gold,and it is given that no gold is silver.  So, glittering element can never be silver Here (1) follows

Comments

@Praggy Sir.

If glitters is an empty set, then how it is possible that All that glitters is gold.

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srestha mam according to me and you ans is e but best ans say ans is a so which is right ans ?

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One thing sure according to IBPS bank exam option e is correct ......computer science total depend upon logic if miss little bit  you will be wrong way

Answer 3

Gold(X) = X is Gold

Glitter(X) = X glitters

Silver(X) = X is Silver

All that glitters is gold =>   Glitter(X) -> Gold(X)   => $\overline{Glitter(X)} \vee Gold(X)$  .... (1)

No gold is silver  =>          $\overline{Gold(X)} \wedge Silver(X)$ ... (2)

Now from (1) and (2) we got

                                                   $\overline{Glitter(X)} \vee Gold(X)$

                                                  $\overline{Gold(X)} \wedge Silver(X)$

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                                                   $\overline{Glitter(X)} \wedge Silver(X)$            

 

So Option A ...

Answer 4

∀x Glitters(x) ⇒ Gold(x) and ∀x Gold(x) ⇒ ¬Silver(x)

Even if Glitters(x) is false Gold(x) is true so if nothing glitters then also it can be Gold. so, it may so happen that no gold glitters so (2) is not always satisfied.

For(1) there can never be a silver which glitters.

so answer is (a).