Which one of the following statements has the truth value T?

Which one of the following is not true?

The number of binary operations that can be defined on a set of 3 elements is _____________

The identity element in the group {R - {1},x} where a * b = a + b - ab is __________

If p is true and q is false, then which of the following is not true?
(1) p ⟶ q is F
(2) p v q is T
(3) p ∧ q is F
(4) p ⇔ q is F

Which of the following is not a contradiction?
(1) p v q
(2) p ∧ q
(3) p v ~q
(4) p ∧ ~p

Let A =\(\begin{bmatrix} 0 & 1 \\ 1 & 1 \end{bmatrix},B=\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}\)be any two boolean matrices of the same type. Find AvB and A\(\wedge\)B.

Write each of the following sentences in symbolic form using statement variables p and q.
(i) 19 is not a prime number and all the angles of a triangle are equal.
(ii) 19 is a prime number or all the angles of a triangle are not equal
(iii) 19 is a prime number and all the angles of a triangle are equal
(iv) 19 is not a prime number

Which one of the following sentences is a proposition?
(i) 4 + 7 =12
(ii) What are you doing?
(iii) 3ⁿ ≤ 81, n ∈ N
(iv) Peacock is our national bird
(v) How tall this mountain is!

Show that p v (q ∧ r) is a contingency.

Verify the
(i) closure property,
(ii) commutative property,
(iii) associative property
(iv) existence of identity and
(v) existence of inverse for the arithmetic operation - on Z.

Construct the truth table for \((p\overset { \_ \_ }{ \vee } q)\wedge (p\overset { \_ \_ }{ \vee } \neg q)\)

In (z, *) where * is defined by a * b = a^b, prove that * is not a binary operation on z.

Using the equivalence property, show that p ↔️ q ≡ ( p ∧ q) v (ㄱp ∧ ㄱq)

Verify (p ∧ ~p) ∧ (~q ∧ p) is a tautlogy, contradiction or contingency.