If statement forms P and Q are logically equivalent, then P ↔ Q is a tautology. Conversely, if P ↔ Q is a tautology, then P and Q are logically equivalent. Use ↔ to convert each of the logical equivalences in 29–31 to a tautology. Then use a truth table to verify each tautology. 29. p → (q ∨ r) ≡ (p ∧ ∼q) → r

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 33 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30 ∘c on monday, but decreased at a constant rate in the next 33 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.

George has seven boxes of five pencils. giulio three boxes of eight pencils. one of the boys arranges all his pencils equally into two groups. was this george or giulio how many are in each group explain

Car a and car b were in a race .the driver of car b claimed that his car was twice as fast as car a