Subtraction is not a binary operation in

Which one of the following statements has truth value F?

Which one is the contrapositive of the statement (pVq)⟶r?

The identity element of \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\} \) |x \(\in \) R, x ≠ 0} under matrix multiplication is __________

Which of the following is a contradiction?

How many rows are needed for following statement formulae?
(( p ∧ q) ∨ (¬r ∨¬s)) ∧ (¬ t ∧ v))

Determine whether ∗ is a binary operation on the sets given below.
(a*b) = a√b is binary on R

Construct the truth table for the following statements.
​​​​​​¬p ∧ ¬q

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

Let G = {1, w, w²) where w is a complex cube root of unity. Then find the universe of w². Under usual multiplication.

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.

Define an operation∗ on Q as follows:  a*b = \(\left( \frac { a+b }{ 2 } \right) \); a,b ∈Q. Examine the existence of identity and the existence of inverse for the operation * on Q.

Show that p ➝ q and q ➝ p are not equivalent

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

Construct the truth table for (-p) v (q ∧ r)

Establish the equivalence property connecting the bi-conditional with conditional: p ↔️ q ≡ (p ➝ q) ∧ (q⟶ p)

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

Construct the truth table for (p ∧ q) v r.

In (N, *) where * is defined by x * y = max (x, y) check the closure axion and identity anion.