======Discrete Structures Knowledge Assessment====== =====Overview===== We have been going full force with our explorations of topics these past few weeks. Just to make sure we are all retaining this information, please complete the following (via **gimmeh**) by the due date. =====0x0: Basic Logic===== Say we had the following truth table: ^ P ^ Q ^ R ^ X | | F | F | F ^ F | | F | F | T ^ F | | F | T | F ^ T | | F | T | T ^ F | | T | F | F ^ T | | T | F | T ^ F | | T | T | F ^ T | | T | T | T ^ F | NOTE: P, Q, R are inputs; X is output What logic operation is being described? - AND - OR - NOR - XNOR =====0x1: Logical Derivation===== Say we had the following truth table: ^ P ^ Q ^ R ^ X ^ Y | | F | F | F ^ T ^ T | | F | F | T ^ T ^ F | | F | T | F ^ F ^ T | | F | T | T ^ F ^ F | | T | F | F ^ T ^ T | | T | F | T ^ T ^ F | | T | T | F ^ F ^ T | | T | T | T ^ F ^ T | NOTE: P, Q, R are inputs; X, Y are outputs (and independent outputs at that) What functions are X and Y accomplishing? - X: AND, Y: OR - X: sum, Y: carry - X: mean, Y: mode - X: NOT Q, Y: NAND =====0x2: Set Properties===== Let's say we had the following sets: A = { PRIMES } B = { 11, 13, 17, 19 } Which statement can be considered true? - set difference of A and B is A - intersection of A and B is A - union of A and B is A - union of A and B is B =====0x3: Set Operations===== Let's say we had the following sets of colors: A = { red, yellow, blue } B = { orange, green, purple } C = { green, yellow } What would give us the set containing just the colors red and blue? - C INTERSECTION A - (C UNION (A - C)) - (A - C) - C INTERSECTION B