Question
Examine whether the following logical statement pattern is tautology, contradiction or contingency.
$[(p \rightarrow q) \wedge q] \rightarrow p$
$[(p \rightarrow q) \wedge q] \rightarrow p$
Consider the statement pattern : [(p → q) ∧ q ] → p
No. of rows = 2n = 2 × 2 = 4
No. of column = m + n = 3 + 2 = 5
Thus the truth table of the given logical statement:
[(p → q) ∧ q] → p
| P | q | $p \rightarrow q$ | $(p \rightarrow q) \wedge q$ | $[(p \rightarrow q) \wedge q] \rightarrow p$ |
| T | T | T | T | T |
| T | F | F | F | T |
| F | T | T | T | F |
| F | F | T | F | T |
The entries in the last column of the above truth table are neither all T nor all F.
∴ [(p → q) ∧ q] → p is contingency.
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is $\frac{1}{2}[\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}]$
Question is modified.
Show that the area of a triangle $A B C$, the position vectors of whose vertices are $\bar{a}, \bar{b}$ and $\bar{c}$
is $\frac{1}{2}[\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}]$.