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

Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
\(a*b=\left( \frac { a-1 }{ b-1 } \right) ,\forall a,b\in Q\)

Identify the valid statements from the following sentences.

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 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?
\(p \vee \neg t \wedge(p \vee \neg s)\)

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.

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.

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

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

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

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

*	a	b	c
a	b
b	c	b	a
c	a		c

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 ∧ ¬q

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

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

Construct the truth table for the following statements.
(¬p ⟶ r) ∧ ( p ↔️ q)

Write the converse, inverse, and contrapositive of each of the following implication.
If a quadrilateral is a square then it is a rectangle.