A binary operation on a set S is a function from

In the set Q define a⊙b = a+b+ab. For what value of y, 3⊙(y⊙5) = 7?

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

Which of the following is a tautology?

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

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.

Let p: Jupiter is a planet and q: India is an island be any two simple statements. Give verbal sentence describing each of the following statements.
(i) ¬p
(ii) p ∧ ¬q
(iii) ¬p ∨ q
(iv) p➝ ¬q
(v) p↔q

In the set of integers under the operation * defined by a * b = a + b - 1. Find the identity element.

Let S be the set of positive rational numbers and is defined by a * b = \(\frac{ab}{2}\). Then find the identity element and the inverse of 2.

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_e = the set of all even integers

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

Let \(A=\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \end{matrix}\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix} \right) ,B=\left( \begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 0 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix} \right) ,C=\left( \begin{matrix} 1 & 1 \\ 0 & 1 \\ 1 & 1 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 1 \end{matrix} \right) \)be any three boolean matrices of the same type.
Find (A∨B)∧C 

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)

How many rows are needed for following statement formulae?
\(p \vee \neg t \wedge(p \vee \neg s)\)

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