# Question: 1 express the following proposition in a symbolic form by...

###### Question details

1. Express the following proposition in a symbolic form by defining atomic propositions and construct a truth table for the expression.

“If you enter the password correctly then you do not subscribe to the Web”

Is it tautology, contradiction, or neither?

2. Use the laws of logic to simplify (¬p Ʌ ¬ q) ᴠ (p Ʌ ¬q) as far as possible.

3. Let x be any one of the four students in a college.

Tam attended only Lecture 1.

Ramie attended both Lecture 1 and Lecture 2.

Vim attended only Lecture 2.

Sam attended neither of the Lectures.

Let F(x) be “x attended Lecture 1” and B(x) be “x attended Lecture 2”, where x denotes one of the above students. Rewrite the following statements in simple English sentences and use the above information to determine its truth values.

(a) ꓱ x such that F(x) ꓥ B(x).

(b) ꓯ x, F(x) ꓦ B(x)

(c) ꓱ x such that ¬ (F(x) ꓦ B(x))

4. Prove that if x2+2 is even then x is even.