Tag: discrete mathematics
Questions Related to discrete mathematics
Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows:
(i) $a\ast b = a - b$ (ii) $a\ast b = a^{2} + b^{2}$
(iii) $a\ast b = a + ab$ (iv) $a\ast b = (a - b)^{2}$
(v) $a\ast b = \dfrac {ab}{4}$ (vi) $a\ast b = ab^{2}$
Find which of the binary operations are commutative and which are associative
State whether the following statements are true of false. Justify.
(i) For an arbitrary binary operation $\ast$ on as set $N, a\ast a = a\forall a \epsilon N$
(ii) If $\ast$ is a commutative binary operation on $N$, then $a\ast (b\ast c) = (c\ast b) \ast a$
Consider a binary operation $\ast$ on $N$ defined as $a\ast b = a^{3} + b^{3}$. Choose the correct answer
Let $$ be a binary operation defined on the set of rational numbers $Q$ defined by $a * b= ab + 1,$ in this statement $$ is a commutative.
Consider the following statements for non empty sets A, B and C
1 $\displaystyle A-\left ( B-C \right )=\left ( A-B \right )\cup C $
2 $\displaystyle A-\left ( B\cup C \right )=\left ( A-B \right )- C $
which of the statements given above is/are correct?
If A, B, C are any three sets, $A-(B\cup C)$ will be
Identify the associative law of union.
Sum of $(267 + 345) + 21$ and $267 + (345 + 21)$ will be same.
The set of integers $Z$ with the binary operation $*$ defined as $a * b = a + b+ 1$ for $a, b, Z$ is a group. The identity element of this group is
If the binary operation $*$ is defined on a set of ordered pairs of real numbers as $(a, b) * (c, d) = (a \times d + b \times c, b \times d)$ and is associative, then $(1, 2) * (3, 5) * (3, 4)$ is equal to