MTH104 Solved Quiz 4 by Iqra Azhar

Let S be a partially ordered set, and let A be a subset of S. If A has an upper bound ,we say A is bounded above. Select the correct option

Let S be a partially ordered set, and let A be a subset of S. An element m in S is called an upper bound of A if m succeeds every element of A, that is, for every x ϵ A, we have x ≤ m.

Select the correct option

If an upper bound of A succeeds every other upper bound of A, then it is called the supremum of ASelect the correct option

Let S be a partially ordered set, and let A be a subset of S. If A has a lower bound we say A is bounded below. Select the correct option

set S(A) denote the collection of all initial segments of elements in a well-ordered set A, and let S(A) be ordered by set inclusion. Then A is similar to S(A) and, in particular, the function f : A →S(A) defined by f(x) = s(x) is a similarity mapping between A and S(A).

Select the correct option The ordinal number of set {1,2,3} is _____________.Select the correct option

Suppose A and B are well-ordered sets, and suppose A is similar to an initial segment of B. Then A is said to be _________ than B.Select the correct option

Longer

shorter

The correct option is shorter.

Let A be a well-ordered set. Then every subset of A is well-ordered. Select the correct option

set S be a partially ordered set, and let A be a subset of S. An element n in S is called a lower bound of A if n precedes every element of A, that is, for every y ϵ A, we have y ≥ n.Select the correct option

The ordinal number of {1,2,3,4} is _________.Select the correct option The ordinal number of empty set is __________.Select the correct option

Let A be a well-ordered set. The initial segment s(a) of an element a ϵ A consists of all elements in A which strictly precedes a.Select the correct option

The ordinal number of the set P of counting numbers is denoted by ω.Select the correct option

True

false

Suppose X and Y are partially ordered sets. A one-to-one(injective) function f :X → Y is called a similar mapping from X into Y if f preserves the order relation, that is, if the following conditions holds for any pair a, b ϵ X: a ≤ b in X if and only if f(a) ≤ f(b) in Y.Select the correct option

The ordinal number of set {a,{b,c}} is __________________.Select the correct option