@lindyk8, the first premise reads: A implies B, which also means B will only happen if, and only if, A happens; it can also read “if A then B”. The second premise reads the negation of B, or “not” B, which means B didn’t occur. Given premise 1, which states that A implies B, and premise 2, which states that B didn’t occur, we can conclude with absolute certainty that A didn’t occur.
Think of it this way: A = I live in San Francisco, B = I live in California.
If I live in S.F. then I live in California (A -> B)
I don’t live in California (~B)
Therefore, I don’t live in S.F. (~A)
You can replace A and B with any valid claims and the argument will always be sound.