Given a statement: For every student $x$ if $x$ likes Math and enjoys programming then $x$ is a CS major.

a$.$ Write its Negation $($in English$)-$ Show all your work!

b$.$ Write its Contrapositive $($in English$)-$ Show all your work!

c$.$ Write its Converse $($in English$)-$ Show all your work!

d$.$ Write its Inverse $($in English$)-$ Show all your work!

Write Negations $($in English$)$ for the following statements. Show all your work!

a$.$ For every person $x$ there is a fruit $f,$ there is a vegetable $v$ such that $x$ likes $f$ or has not tried $v.$

b$.$ There is a color $y$ such that every human $p$ likes the color $y$ and is happy wearing it $(y).$

Given an argument. Verify its validity $($Prove$/$Disprove$)$ using Venn diagram. $-$ Show all your work! Make a conclusion $($Is it Valid? Is it Invalid?$)!$

All healthy people eat vegetables.

All healthy people like fruits.

:$.$ All people that eat vegetables like fruits.