Given the symbolic meanings: A @ B A@B A @ B means "All A are B" A&B means "Only a few A are B" A A A $B$ means "No A is ...

Question

Given the symbolic meanings:

  • A@BA@B means "All A are B"
  • A&B means "Only a few A are B"
  • AA$B$ means "No A is B"
  • A%BA%B means "Some A is B"

Consider the statement:

F%J</mi><mi>G</mi><mi mathvariant="normal">&amp;</mi><mi>C</mi><mi mathvariant="normal">@</mi><mi>E</mi></mrow><annotation encoding="application/x-tex">F \% J \ G \& C @ E

Evaluate the following conclusions:

I. All C can never be F

II. Some G is not E

III. All F being G is not a possibility

IV. Some J being E is a possibility

Which of the following conclusions logically follow from the given statement?

Options

A.

Both III and IV

B.

Only I

C.

Both II and III

D.

Only IV

E.

Only III

syllogismlogical reasoningsymbol basedbanking exam

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