A truth table is a table that lists all possible combinations of input values for a logical expression and their corresponding output values. It is used to determine the truth value of a logical expression for all possible combinations of its variables. A truth table typically consists of a row for each possible combination of … Read more
The symmetric difference of two sets A and B, denoted by A Δ B, is the set of all elements that are in A or B, but not in both. Formally, A Δ B = {x | (x ∈ A and x ∉ B) or (x ∉ A and x ∈ B)} In other words, … Read more
The difference of two sets A and B, denoted by A – B, is the set of all elements that are in A but not in B. Formally, A – B = {x | x ∈ A and x ∉ B} In other words, the difference of two sets consists of all elements that are … Read more
The power set of a set A, denoted by P(A), is the set of all subsets of A, including the empty set and A itself. For example, if A = {1, 2}, then P(A) = { {}, {1}, {2}, {1,2} }. The power set of a set can be useful in various areas of mathematics, … Read more
The Cartesian product of two sets A and B, denoted by A x B, is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. Formally, A x B = {(a, b) | a ∈ A, b ∈ B} For example, if A = {1, 2} and … Read more
In mathematics, the intersection of two or more sets is a new set that contains only the elements that are common to all the original sets. The intersection of sets is represented by the symbol ∩. For example, if we have two sets A = {1, 2, 3} and B = {2, 3, 4}, then … Read more
In mathematics, the union of two or more sets is a new set that contains all the distinct elements of the original sets. The union of sets is represented by the symbol ∪. For example, if we have two sets A = {1, 2, 3} and B = {2, 3, 4}, then the union of … Read more
In set theory, the power set (or the “set of all subsets”) of a given set is defined as the set of all possible subsets of that set, including the empty set and the set itself. For example, if we have a set A = {1, 2}, the power set of A would be: P(A) … Read more
To calculate the total number of bits from 1 to n, we can iterate over all the numbers from 1 to n and count the number of bits in each number. We can use the Integer.bitCount() method in Java or the countOneBits() method in Kotlin to count the number of bits in each number. Then, … Read more
