Universal Modus Tollens Rule

Discrete Mathematics: Universal Modus Tollens Rule
Topics discussed:
1) The Universal Modus Tollens Rule.
2) An example based on Universal Modus Tollens Rule.

Music:
Axol x Alex Skrindo - You [NCS Release]

#DiscreteMathematicsByNeso #DiscreteMaths #UniversalModusTollensRule

[the_ocean_eyes]

1) Let, P - x is computer science major.
Q - x is taking discrete maths course.

For all P(x) -> Q(x)
Q(riya)
P(riya) -> Q(riya) -By universal

So, P(riya) - Fallacy

2) Let, P - x eats granola everyday.
Q - x is healthy.
For all P(x) -> Q(x)
~ Q(Linda)
P(Linda) -> Q(Linda) -By universal

So, ~ P(Linda) -Modus Tollens

[SamSam-gxql]

1.) False (Fallacy of Affirming Conclusion)
2.) True (Universal Modus Tollens)

[rajeshprajapati]

Finished Chapter 1 and Chapter 2. Thank you so much !!

[JD-ebqu]

1.)I think 1st sentence false
2.)1. For all x{p(x)->q(x)} -premise
2. ~q(linda)-premise instantiation from 1]
4.~p(linda)[modus stollen from 2, 3]
~p(linda)
So this is TRUE according to UNIVERSAL MODU'S STOLLEN RULE
Sir thanks a lot indeed sir this is very useful to me my text book couldn't help to me but your explanation is helpful very much 👌🙏🙏🙏

[saswateesahoo]

Thank you so much sir for this amazing explanation

[saimalli]

Let p(x) denotes "x is a computer science"
Q(x) denotes "x takes discrete mathematics course"
a)1.forall x(p(x)->q(x)) premise
2.p(ria) premise
3.p(ria)->q(ria)
(by universal Instantiation (1))
4.q(ria) (by modus ponens from2&3)

[jayxcoder]

a) False, Fallacy of affirming the conclusion.
b) True, Universal Modus Tollens

[acriziosouza]

Modus Ponens: p -> q OR [(p -> q) ^ p] -> p
p

q

Modus Tollens: p -> q OR [(p -> q) ^ ¬q] -> ¬p
¬q

¬p

Universal Instantiation: this rule is used to conclude that P(c) is true when ∀xP(x) is true.
∀xP(x)

P(c)

A) Let P(x) denotes "x is a computer science major"
Q(x) denotes "x takes discrete mathematics course"

∀x(P(x) -> Q(x)) Premise
Q(Ria) Premise
P(Ria) -> Q(Ria) By universal instantiation from (1)
P(Ria) = ? Fallacy -> Affirming the consequence (Ria could take discrete mathematics course and not being a computer science major)

B) Let P(x) denotes "x eats granola everyday"
Q(x) denotes "x is healthy"

∀x(P(x) -> Q(x)) Premise
¬Q(Linda) Premise
P(Linda) -> Q(Linda) By universal instantiation from (1)
¬P(Linda) Modus tollens from (2) and (3)

[CHATUR__RAMALINGAM]

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[harshsharma]

First is false and second one is true ?

[shivajichalise_]

HELP!
Everyone in math class loves proof. Someone in math class have never taken calculus. Conclusion Someone who loves proof have never taken calculus.

[gamexd]

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"Thanks"