If v.s. Only If v.s. If and Only If (Iff) If I get 90+ in the final, then I get an A for this course. -- 90+ in the final is sufficient for an A, but may not be necessary. I get an A for this course only if I get 90+ in the final. -- 90+ in the final is necessary for an A, but may not be sufficient. I get an A for this course if and only if I get 90+ in the final. -- 90+ in the final is “equivalent” to an A. (necessary and sufficient)

Or v.s. Exclusive Or Or: p  q Exclusive Or: p⊕q ≡ (p  q)  ~(p  q) I need to get 90+ in the final, or I won’t get an A. -- “get 90+ in the final” or “not get an A” Or Exclusive Or

Negation Write the negation of −3≤𝑥<1. −3≥𝑥>1 ? −3>𝑥≥1 ? It should be 𝑥<−3  𝑥≥1 !! −3≤𝑥<1 is equivalent to “𝑥≥−3 and 𝑥<1”, so by De Morgan’s law, its negation should be “𝑥<−3 or 𝑥≥1”.