(Solved): 5. Let \( b \) be a fixed integer and \( j \) a fixed positive integer. Show that if \( P(b), P(b+ ...

5. Let \( b \) be a fixed integer and \( j \) a fixed positive integer. Show that if \( P(b), P(b+1), \ldots, P(b+j) \) are true and \( [P(b) \wedge P(b+1) \wedge \cdots \wedge P(k)] \rightarrow P(k+1) \) is true for every integer \( k \geqslant b+j \), then \( P(n) \) is true for all integers \( n \) with \( n \geqslant b \).