A binary operation on a set S is a function from

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

Which one of the following statements has truth value F?

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

Which one of the following is incorrect? For any two propositions p and q, we have

On Z, define \(⊗ \mathrm{by}(m * n)\) = mn + nm: ∀m, n∈Z. Is ⊗ binary on Z?

Let \(*\) be defined on R by (a \(*\) b) = a + b + ab - 7. Is \(*\) binary on R? If so, find 3 \(*\)\(\left( \frac { -7 }{ 15 } \right) \).

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

Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
a*b = a + 3ab − 5b²; ∀a,b∈Z

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.

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.

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

Consider p→q : If today is Monday, then 4 + 4 = 8.