in Mathematical Logic
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plz someone explain what is the diference between option (b)& (c)

in Mathematical Logic
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1 Answer

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(B) $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) ∧ \text{likes}\left(y,x\right)\right]\right]$

For every Person,if the person is a teacher ,then there exists some student who loves the teacher$\Rightarrow$Every teacher is liked by some student.


(C) $∃(y) ∀(x)\left[\text{teacher}\left(x\right) → \left[\text{student}\left(y\right) ∧ \text{likes}\left(y,x\right)\right]\right]$

There exists some person who is student who loves all the teacher$\Rightarrow$Some students love  all the teacher.

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so both op(b)& (c) there english statements are same.I thing there is no any difference between both 2 english statements.
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