GNED 1101 Chapter Notes - Chapter 1.2: Sentence Clause Structure, If And Only If, Logical Biconditional

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Section 1.2 Compound Statements and Connectives
Compound Statements
“iple “tateets eah oey oe idea ith o oetig ods You’e ealthy, You’e ell eduated
Statements that are formed by combining two or more simple statements are called compound statements
o Words called connectives are used to join these simple statements together.
o Coetie ods ilude; ad, o, if….the, if ad oly if
And Statements
If to siple stateets ae oeted usig the oetie ad, ad is syolially epeseted y
The compound statement formed by using the word and is called a conjunction
Example Simple Sentences into a compound sentence
o P: It is after 5pm
o Q: They are Working
COMPOUNDED - It is after 5pm and they are working
Symbolically illustrated as p q
o Compounded with Negation
It is after 5pm and they are not working
Symbollically illustrated as p q
The symbol fo ad a also e taslated as ut, yet, nevertheless
o It is after 5pm and they are working
o It is after 5pm, but they are working
o It is after 5pm, yet they are working
o It is after 5pm, nevertheless they are working
Or Statements
Or as a connective has two meanings
o I visited London or Paris means I visited London or Paris but not both
This is an exclusive or, which means one or the other, but not both
o I visited London or Paris or both
This is an inclusive or, which means either or both
In mathematics, the use of the connective or means the inclusive or. If p and q represent two simple
stateets, the the opouded stateet  p o   eas p o  o oth.
Or as a connective is called a disjunction and is symbolized by
Thus, the opoudd stateet p o  o oth a y syolized as p q.
Example
o The ill eeies ajoity appoal o the ill eoes la a e syolized as p q
o The ill eeies ajoity appoal o the ill does ot eoe a la a e syolized as pq
If-Then Statements
If p, then q
If-then is symbolized by
If-then is thus a conditional statement
In a conditional statement, the statement before the is called the antecedent, and the statement after the
is called the consequent
o Antecedent Consequent
Example:
o P: A person is a father
o Q: A person is a male
A few options:
If a person is a father, then that person is a male is symbolized as pq
If a person is a male, then that person is a father is symbolized as qp
If a person is not a male, then that person is not a father is symbolized as:
q p
If-Then can also be translated differently
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I(cid:373)ple tate(cid:373)e(cid:374)ts ea(cid:272)h (cid:272)o(cid:374)(cid:448)ey o(cid:374)e idea (cid:449)ith (cid:374)o (cid:272)o(cid:374)(cid:374)e(cid:272)ti(cid:374)g (cid:449)o(cid:396)ds (cid:894)(cid:862)you"(cid:396)e (cid:449)ealthy(cid:863), (cid:862)you"(cid:396)e (cid:449)ell edu(cid:272)ated(cid:863)(cid:895) Statements that are formed by combining two or more simple statements are called compound statements: words called connectives are used to join these simple statements together, co(cid:374)(cid:374)e(cid:272)ti(cid:448)e (cid:449)o(cid:396)ds i(cid:374)(cid:272)lude; a(cid:374)d, o(cid:396), if . the(cid:374), if a(cid:374)d o(cid:374)ly if. If t(cid:449)o si(cid:373)ple state(cid:373)e(cid:374)ts a(cid:396)e (cid:272)o(cid:374)(cid:374)e(cid:272)ted usi(cid:374)g the (cid:272)o(cid:374)(cid:374)e(cid:272)ti(cid:448)e (cid:862)a(cid:374)d(cid:863), a(cid:374)d is sy(cid:373)(cid:271)oli(cid:272)ally (cid:396)ep(cid:396)ese(cid:374)ted (cid:271)y . The compound statement formed by using the word and is called a conjunction. Example simple sentences into a compound sentence: p: it is after 5pm, q: they are working. Compounded - it is after 5pm and they are working. Symbolically illustrated as p q: compounded with negation. It is after 5pm and they are not working. The symbol fo(cid:396) (cid:862)a(cid:374)d(cid:863) (cid:272)a(cid:374) also (cid:271)e t(cid:396)a(cid:374)slated as (cid:271)ut, yet, nevertheless. It is after 5pm and they are working. It is after 5pm, but they are working. It is after 5pm, yet they are working.

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