1) Composition of functions: This is a concept in mathematics where two functions are combined to form a third function. If we have two functions, say f(x) and g(x), the composition of these functions, denoted as (f∘g)(x) or f(g(x)), is the function that first applies g to an argument and then applies f to the result.

2) Monoid: A monoid is a set equipped with an associative binary operation and an identity element. In simpler terms, it's a mathematical structure where you can combine any two elements in a certain way to get another element in the set, and there's a special "do nothing" element that doesn't change any element when combined with it.

3) Existential Quantifier: In logic, an existential quantifier is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the symbol ∃. For example, the statement "∃x P(x)" means "there is at least one x such that P(x) is true".

4) Partially Ordered Set: A partially ordered set (also poset) is a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other. This relation must be reflexive (every element is related to itself), antisymmetric (if a is related to b and b to a then a and b are the same element) and transitive (if a is related to b and b to c then a is related to c).

5) Boolean Algebra: Boolean algebra is a subarea of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. It is used in logic gates and circuits, which are the basis of computer hardware.

6) Tree: In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.

7) Complete Graph: A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of different vertices is connected by a pair of unique edges in both directions.

Question

1) Composition of functions: This is a concept in mathematics where two functions are combined to form a third function. If we have two functions, say f(x) and g(x), the composition of these functions, denoted as (f∘g)(x) or f(g(x)), is the function that first applies g to an argument and then applies f to the result.

2) Monoid: A monoid is a set equipped with an associative binary operation and an identity element. In simpler terms, it's a mathematical structure where you can combine any two elements in a certain way to get another element in the set, and there's a special "do nothing" element that doesn't change any element when combined with it.

3) Existential Quantifier: In logic, an existential quantifier is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the symbol ∃. For example, the statement "∃x P(x)" means "there is at least one x such that P(x) is true".

4) Partially Ordered Set: A partially ordered set (also poset) is a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other. This relation must be reflexive (every element is related to itself), antisymmetric (if a is related to b and b to a then a and b are the same element) and transitive (if a is related to b and b to c then a is related to c).

5) Boolean Algebra: Boolean algebra is a subarea of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. It is used in logic gates and circuits, which are the basis of computer hardware.

6) Tree: In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.

7) Complete Graph: A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of different vertices is connected by a pair of unique edges in both directions.

Knowee AI · Accepted Answer

1) Composition of functions: This is a concept in mathematics where two functions are combined to form a third function. If we have two functions, say f(x) and g(x), the composition of these functions, denoted as (f∘g)(x) or f(g(x)), is the function that first applies g to an argument and then applies f to the result.

2) Monoid: A monoid is a set equipped with an associative binary operation and an identity element. In simpler terms, it's a mathematical structure where you can combine any two elements in a certain way to get another element in the set, and there's a special "do nothing" element that doesn't change any element when combined with it.

3) Existential Quantifier: In logic, an existential quantifier is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the symbol ∃. For example, the statement "∃x P(x)" means "there is at least one x such that P(x) is true".

4) Partially Ordered Set: A partially ordered set (also poset) is a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other. This relation must be reflexive (every element is related to itself), antisymmetric (if a is related to b and b to a then a and b are the same element) and transitive (if a is related to b and b to c then a is related to c).

5) Boolean Algebra: Boolean algebra is a subarea of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. It is used in logic gates and circuits, which are the basis of computer hardware.

6) Tree: In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.

7) Complete Graph: A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of different vertices is connected by a pair of unique edges in both directions.

1) Composition of functions2) Monoid3) Existential Quantifier4) Partially Ordered Set5) Boolean Algebra6) Tree7) Complete Graph

Question

1) Composition of functions

2) Monoid

3) Existential Quantifier

4) Partially Ordered Set

5) Boolean Algebra

6) Tree

7) Complete Graph

Solution

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