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Description

Pretty sure Makima woke something in me regarding women in suits, or in this case a labcoat https://t.co/0TSnuY1P4v

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Twilights-Secret
Thread Starter - DiaperPony General [NSFW]
Wallet After Summer Sale -
Not a Llama - Happy April Fools Day!
Artist -

Comfy Pones
Okay, the implication on lines 4 and 5 follows from the equality statement on line 1, but I’m confused about what’s going on on lines 2 and 3.
Line 2 is true if A OR B OR C are true - if any of them are true.
Line 3:
(x is an element of A OR B) AND (x is an element of A AND C)
Line 3 is only true if A AND C are both true. In fact, the first part of that statement (x is an element of A OR B) is entirely redundant since it’s always true if the other part of the AND is true (x is an element of A AND C), but whether or not B is true never changes the truth value of the entire statement.
In other words,
(x is an element of A OR B) AND (x is an element of A AND C) = (x is an element of A AND C)
Since both statements are true if and only if A AND C are both true, so they both have identical truth tables.
But line 1 shows you a principle which you apply to line 4 and you end up with line 5. So that makes sense.
Though I think it would be more correct to use = or <=> at the end of line 4 since lines 4 and 5 are equivalent. (They’ll both always have the same truth value, though, so technically, line 4 -> line 5 will never be false, since you’ll never have <line 4 be true and line 5 be false>, but you’ll never have <line 5 be true and line 4 be false>, either, so equality or double implication would convey more information so I say that would be more correct.)
But lines 2 and 3 have no continuity with the other lines, so what’s with those?