MATM LESSON 2

Question 1

a system of conventional spoken, manual (signed), or written symbols by means of which human beings, as members of a social group and participants initsculture, express themselves.

Answer 1

Language

Question 2

Language itself is:

Answer 2

• Precise
• Concise
• Powerful

Question 3

It can make very fine distinctions among set of symbols

Answer 3

Precise

Question 4

It can briefly express long sentences

Answer 4

Concise

Question 5

It gives upon expressing complex thoughts

Answer 5

Powerful

Question 6

A ___ in mathematics is a collection of well defined and distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics

Answer 6

set

Question 7

• Provides a list of all elements
• Example {1,2,3,4}
• Suits for sets with a lesser number of elements
• Easy to understand

Answer 7

Roster Form

Question 8

• Defines the set by using a logical condition
• Suits for sets with more elements
• Little tricky for non-math people

Answer 8

Set Builder Form

Question 9

Tells how many things are in a set. When counting a set of objects, the last word in the counting sequence names the quantity for that set.

Answer 9

Cardinality

Question 10

• the TOTALITY of ALL the elements in two or more given sets
• denoted by ‘‘U’’

Answer 10

Universal Set

Question 11

has no elements, it is empty. Its cardinal number is zero.

Answer 11

Null Set

Question 12

• is the combination of elements of two or more sets
• Example: A={1,2,3,4} and B={1,5,6,7}
  then
  A ∪ B = {1,2,3,4,5,6,7,}

Answer 12

UNION SET

Question 13

• it refers to the common elements of the 2 given sets
  -Example: A={a,b,c,d,e} and B={a,e,i,o,u}
  then
  A ∩ B = {a,e}

Answer 13

INTERSECTION OF SETS

Question 14

• it refers to the elements of 1st set alone but not an element of other set.
• Example: Find A-B and B-A
  A={1,2,3,4,5} and B={2,4,6,8,10}
  then
  A – B = {1,3,5}
  B – A = {6,8,10}

Answer 14

DIFFERENCE OF SETS

Question 15

• refers to the elements of the universal set alone which is not part of the concerned set.
• If U={a, b, c, d, e, f, g, h, u, j}
  and A={a, e, i}

A’ ={b, c, d, f, g, h, j}

Answer 15

COMPLEMENTARY OF SETS

Question 16

– a set is subset if all its elements are can be found to other sets.
- “⊆” – “is a subset of”. (equally the same)
“⊂” – “is a proper subset of”.
A={1,2,3,4} B ⊂ A
B={1,2,3} C ⊄ A
C={3,4,5} D ⊆ A
D={2,1,4,3}

Answer 16

SUBSET OF SETS

Question 17

• sets are equal if they have the exactly the same elements
• M={1,3,9,5,−7} andN={5,−7,3,1,9} therefore M=N

Answer 17

Equal sets

Question 18

• sets are equivalent if they have same number of elements
• ## S={1,2,3} andT={a,b,c} therefore S∼T

Answer 18

Equivalent Sets

Question 19

serves as a set of rules that govern the structure and presentation of mathematical proofs.It allows us to determine the validity of arguments in and out of mathematics.

Answer 19

Logic

Question 20

is a statement that is, by itself, either true or false. They can be expressed in symbols P, Q, R, or p, q, r.

Answer 20

proposition

Question 21

• means single idea statement

Answer 21

a. Simple

Question 22

• conveys two or more ideas

Answer 22

b. Compound

Question 23

is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both.

Answer 23

Proposition

Question 24

Not ~p

Answer 24

Negation

Question 25

And P ^ Q

Answer 25

Conjunction

Question 26

Or P V Q

Answer 26

Disjunction

Question 27

If…Then P → Q

Answer 27

Conditional

Question 28

If and only if P ↔ Q

Answer 28

Bi-conditional

Question 29

“for all” or “for every”, denoted by ∀

Answer 29

Universal Quantifier

Question 30

“there exists”, denoted by ∃

Answer 30

Existential Quantifier

Question 31

p → q If p, then q

Answer 31

Conditional Statement

Question 32

q → p If q, then p

Answer 32

Converse

Question 33

~p → ~q If not p, then not q

Answer 33

Inverse

Question 34

~q → p If not q, then not p

Answer 34

Contrapositive

Question 35

If True then False If False then True

Answer 35

Negation ~p

Question 36

If theres two True, then True If theres a single False then automatically False

Answer 36

Conjunction p ^ q

Question 37

If theres two False, then False If theres a single True then automatically True

Answer 37

Disjunction p v q

Question 38

# My Theory If False is last then F (T, F = T)

Answer 38

Conditional p → q

Question 39

If different then False (T, F = F) (F,T = F) If same then True ( F, F = T)

Answer 39

Bi conditional p ↔ q