Prove the following sequents. [50 points]
a. (a ʌ b) ʌ c ͱ a ʌ (b ʌ c)
b. p ͱ q → (p ʌ q)
c. (p → q) ʌ (q → r) ͱ p ʌ q → r
d. p → (q ʌ r) ͱ (p → q) ʌ (p → r)

Suppose s, t, and w are strings that have already been created inside main. write a statement or statements, to be added to main, that will determine if the lengths of the three strings are in order by length, smallest to largest. that is, your code should determine if s is strictly shorter than t, and if t is strictly shorter than w. if these conditions hold your code should print (the boolean value) true. if not, your code should print false. (strictly means: no ties) example: if s, t, and w are "cat", "hats", and "skies" your code should print true - their lengths are 3-4-5; but if s, t, and w are "cats" "shirt", and "trust", then print false - their lengths are 4-5-5 enter your code in the box below

You can apply several different worksheet themes from which tab?

What is the biggest difference between section breaks and regular page breaks