Search & Filtering
a) Suppose P (x, y) denotes the equation y=x+8, what will the truth values of the Propositions P (2,2), P (0,4).
If the statement q ^ r is true, determine all combinations of truth values for p and s such that the statement (q -> [¬p v s]) ^ [¬s -> r] is true.
let q(x) denote the statement x is an integer . what are the truth values of the following?
((~a^b)^(b^c)^~b
Use any of the two proof methods to prove:
((~a^b)^(b^c))^~b
Exercise 9:
Draw a full binary tree having the following properties
1. Four internal vertices and five terminal vertices.
2. Height = 3 and nine terminal vertices.
3. Height = 4 and nine terminal vertices.
a) Suppose P (x, y) denotes the equation8, what will the truth values of the Propositions P (2, 2), P (0, 4)?
In how many ways can 10 people be seated in a row so that a certain pair of
them are not next to each other?
Three persons enter into car, where there are 5 seats. In how many ways can
they take up their seats?
How many numbers can be formed using the digits 1, 3, 4, 5, 6, 8 and 9 if no
repetition is allowed?
13) Suppose that we draw a card from a deck of 52 cards and replace it before the
next draw. In how many ways can 10 cards be drawn so that the tenth card is a
repetition of a previous draw?
How many different plates are there that involve 1, 2 or 3 letters followed by 1,
2, 3 or 4 digits?
How many 2 digit or 3-digit numbers can be formed using the digits 1, 3, 4, 5, 6,
8 and 9 if no repetition is allowed?
