The operation * defined by \(a * b =\frac{ab}{7}\) is not a binary operation on

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

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

In the last column of the truth table for ¬( p ∨ ¬q) the number of final outcomes of the truth value 'F' are

The proposition p ∧ (¬p ∨ q) is

If * is defined by a * b = a² + b² + ab + 1, then (2 * 3) * 2 is _____________

Which of the following is a contradiction?

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

Define * on Z by a * b = a + b + 1 ∀ a,b \(\in \) Z. Then the identity element of z is ________

If p is true and q is unknown, then _________

'+' is not a binary operation on ___________

'-' is a binary operation on ___________

In (N, *), x * y = max(x, y), x, y \(\in \) N then 7 * (-7)

In (S, *), is defined by x * y = x where x, y \(\in \) S, then

The number of commutative binary operations which can be defined on a set containing n elements is _________

Write the statements in words corresponding to ¬p, p ∧ q , p ∨ q and q ∨ ¬p, where p is ‘It is cold’ and q is ‘It is raining'.

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

Fill in the following table so that the binary operation ∗ on A = {a, b, c} is commutative.

Write the converse, inverse, and contrapositive of each of the following implication.
If x and y are numbers such that x = y, then x² = y²

Construct the truth table for the following statements.
( p V q) V ¬q

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

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))

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 AVB

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 AΛB

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)

Verify 
(i) closure property 
(ii) commutative property
(iii) associative property
(iv) existence of identity, and
(v) existence of inverse for following operation on the given set m*n = m + n - mn; m, n ∈Z

Verify 
(i) closure property 
(ii) commutative property 
(iii) associative property 
(iv) existence of identity and
(v) existence of inverse for the operation +₅ on Z₅ using table corresponding to addition modulo 5.

Verify 
(i) closure property 
(ii) commutative property 
(iii) associative property
(iv) existence of identity and
(v) existence of inverse for the operation ×11 on a subset A = {1, 3, 4, 5, 9} of the set of remainders {0,1, 2, 3, 4, 5, 6, 7, 8, 9,10}

Let A be Q\{1}. Define ∗ on A by x*y = x + y − xy. Is ∗ binary on A? If so, examine the commutative and associative properties satisfied by ∗ on A.

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