Exercise 5.4.3: proving two logical expressions are not logically equivalent. info about prove that the following pairs of expressions are not logically equivalent. (a) p → q and q → p (b) ¬p → q and ¬p ∨ q (c) (p → q) ∧ (r → q) and (p ∧ r) → q (d) p ∧ (p → q) and p ∨ q

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?