A binary operation on a set S is a function from

Which one of the following is a binary operation on N?

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

If a compound statement involves 3 simple statements, then the number of rows in the truth table is

The truth table for (p ∧ q) ∨ ¬q is given below

Which one of the following is true?

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

Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11

Which one of the following is not true?

The binary operation * defined on a set s is said to be commutative if ______

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 __________

The number whose multiplication universe does not exist in C.

'-' is a binary operation on ___________

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

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

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.

Determine whether ∗ is a binary operation on the sets given below.
a*b = min (a, b) on A = {1, 2, 3, 4, 5}

Determine the truth value of each of the following statements
(i) If 6 + 2 = 5 , then the milk is white.
(ii) China is in Europe or \(\sqrt3\) is an integer
(iii) It is not true that 5 + 5 = 9 or Earth is a planet
(iv) 11 is a prime number and all the sides of a rectangle are equal

Show that p v (~p) is a tautology.

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.

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

Write down the
(i) conditional statement
(ii) converse statement
(iii) inverse statement, and
(iv) contrapositive statement for the two statements p and q given below.
p: The number of primes is infinite.
q: Ooty is in Kerala.

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 

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

Show that ¬(p↔️q) ≡ p↔️¬q

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)

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.

Prove that p➝(¬q V r) ≡ ¬pV(¬qVr) using truth table.

Let S be a non-empty set and 0 be a binary operation on s defined by x 0 y = x; x, Y \(\in \) s. Determine whether 0 is commutative and association.