Truth tables for these calculus formulae

In summary, the conversation is about constructing truth tables for two propositional calculus formulae: (p→(~q)) ∧ r and (q→(~p) ∧ r). The author asks for someone to check their solutions, which they believe are correct. The table provided shows the values for p, q, r, (p→(~q)) ∧ r, and (q→(~p) ∧ r) in each row. The author asks if their solution is correct.
  • #1
charmedbeauty
271
0

Homework Statement



Construct truth tables for the two propositional calculus formulae

(p→(~q))[itex]\wedge[/itex]r and q→((~p)[itex]\wedge[/itex]r)

Homework Equations


The Attempt at a Solution



Can some one please check these solutions because I had a look at the answer and it was different but I don't think I am wrong.

Sorry about the layout I tried pasting of a word doc table but did not work out to well.

Just follow the vales with each column respectively.
Code: 
p   ,	q  ,	r  ,	(p(~q)) [itex]\wedge[/itex] r  ,  ((~p) [itex]\wedge[/itex] r)

T	T	T	    F	                     F
T	T	F	    F	                     F
T	F	T	    T	                     T
T	F	F	    F	                     T
F	T	T	    T	                     T
F	T	F	    F	                     F
F	F	T	    T	                     T
F	F	F	    F	                     T
Is this right??
 
Last edited:
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  • #2
charmedbeauty said:

Homework Statement



Construct truth tables for the two propositional calculus formulae

(p→(~q))[itex]\wedge[/itex]r and q→((~p)[itex]\wedge[/itex]

Homework Equations



The Attempt at a Solution



Can some one please check these solutions because I had a look at the answer and it was different but I don't think I am wrong.

Sorry about the layout I tried pasting of a word doc table but did not work out to well.

Just follow the vales with each column respectively.

p , q , r , (p→(~q)) [itex]\wedge[/itex] r , (q→(~p) [itex]\wedge[/itex] r)

T T T F F
T T F F F
T F T T T
T F F F T
F T T T T
F T F F F
F F T T T
F F F F T

Is this right??
To get better spacing use the [code ] tag.

Code: 
p   ,	q  ,	r  ,	(p→(~q)) ∧ r  ,  (q→(~p) ∧ r)

T	T	T	    F	                     F
T	T	F	    F	                     F
T	F	T	    T	                     T
T	F	F	    F	                     T
F	T	T	    T	                     T
F	T	F	    F	                     F
F	F	T	    T	                     T
F	F	F	    F	                     T
 
Last edited:
  • #3
SammyS said:
To get better spacing use the [code ] tag.

Code: 
p   ,	q  ,	r  ,	(p(~q)) ∧ r  ,  ((~p) ∧ r)

T	T	T	    F	                     F
T	T	F	    F	                     F
T	F	T	    T	                     T
T	F	F	    F	                     T
F	T	T	    T	                     T
F	T	F	    F	                     F
F	F	T	    T	                     T
F	F	F	    F	                     T

Ok thanks but is it right?
 

Related to Truth tables for these calculus formulae

1. What is a truth table?

A truth table is a table that shows all possible combinations of truth values for a given set of logical propositions. It is a tool used in logic and mathematics to determine the truth value of complex statements.

2. How do you construct a truth table?

To construct a truth table, you first list all the propositions involved in the statement. Then, you create columns for each proposition and the final result. In each row, you assign truth values (T or F) to the propositions based on their combinations. Finally, you use logical operators (AND, OR, NOT) to determine the overall truth value of the statement in each row.

3. Why are truth tables important in calculus?

Truth tables are important in calculus because they are used to evaluate the truth value of complex logical statements involving mathematical expressions. This is particularly useful in proving theorems and solving problems in calculus.

4. What are the different types of truth tables used in calculus?

The two main types of truth tables used in calculus are propositional truth tables and predicate truth tables. Propositional truth tables are used for propositions involving logical connectives (AND, OR, NOT), while predicate truth tables are used for propositions involving quantifiers (for all, there exists).

5. How can truth tables be used to simplify calculus formulae?

Truth tables can be used to simplify calculus formulae by identifying equivalent statements and reducing them to simpler forms. This can help in solving problems and proving theorems more efficiently.

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