Prepare the truth table of the following statement patterns: ​ i. [(p → q) ^ q] → p ​ii. ​ (p ^ q) (~p) ​

Question

Prepare the truth table of the following statement patterns:

i. [(p \(\rightarrow\) q) \(\land\) q] \(\rightarrow\) p

ii. (p \(\land\)q)\(\rightarrow\) (~p)

iii. (p \(\rightarrow\) q)\(\leftrightarrow\) (~p \(\lor\)q)

iv. (p \(\leftrightarrow\) r) \(\rightarrow\) (q \(\land\) p)

v. (p \(\lor\) ~q) \(\rightarrow\) (r \(\land\) p)

Answer 1

i. [(p → q)∧q]→p

Note: Here, the statement pattern consists of 2 

statements and 3 connectives. Therefore, the truth table has,

Number of rows = 2² = 4 

and number of columns = (2+3) = 5.

ii. (p \(\land\)q)\(\rightarrow\) (~p)

iii. (p \(\rightarrow\) q)\(\leftrightarrow\) (~p \(\lor\)q)

iv. (p \(\leftrightarrow\) r) \(\rightarrow\) (q \(\land\) p)

v. (p \(\lor\) ~q) \(\rightarrow\) (r \(\land\) p)