High School Mathematics Extensions/Logic/Solutions

Logic Compound truth tables exercises 1. NAND: x NAND y = NOT (x AND y) The NAND function x y x AND y NOT (x AND y) 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 2. NOR: x OR y = NOT (x OR y) The NOR function x y x OR y NOT (x OR y) 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 3. XOR: x XOR y is true if and ONLY if either x or y is true. The XOR function x y x OR y 0 0 0 0 1 1 1 0 1 1 1 0 Produce truth tables for: 1. xyz xyzxyz00000010010001101000101011001111 2. x'y'z' xyzx'y'z'00010010010001101000101011001110 3. xyz + xy'z xyzxyz + xy'z00000010010001101000101111001111 4. xz x zxz000010100111 5. (x + y)' x y(x + y)'001010100110 6. x'y' x yx'y'001010100110 7. (xy)' x y(xy)'001011101110 8. x' + y' x yx' + y'001011101110 Laws of Boolean algebra exercises 1. 1. z = ab'c' + ab'c + abc 2. z = ab(c + d) 3. z = (a + b)(c + d + f) 4. z = a'c(a'bd)' + a'bc'd' + ab'c 5. z = (a' + b)(a + b + d)d' 2. Show that x + yz is equivalent to (x + y)(x + z) Implications exercises Decide whether the following propositions are true or false: If 1 + 2 = 3, then 2 + 2 = 5 is false because something that's true implies something that's false If 1 + 1 = 3, then fish can't swim is true because 1+1 is not 3 Show that the following pair of propositions are equivalent : We use truth tables for this The NAND function x y 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 The columns in the table are the same for both propositions, thus they are equivalent. Logic Puzzles exercises Please go to Logic puzzles.