To determine which statement must be true given [tex]$p \Rightarrow q$[/tex] and [tex]$q \Rightarrow r$[/tex], let's analyze the logical implications.
1. Understanding Implications:
- The implication [tex]$p \Rightarrow q$[/tex] means that if [tex]$p$[/tex] is true, then [tex]$q$[/tex] must also be true.
- The implication [tex]$q \Rightarrow r$[/tex] means that if [tex]$q$[/tex] is true, then [tex]$r$[/tex] must also be true.
2. Combining Implications:
- Since [tex]$p \Rightarrow q$[/tex] implies [tex]$p$[/tex] leads to [tex]$q$[/tex], and [tex]$q \Rightarrow r$[/tex] implies [tex]$q$[/tex] leads to [tex]$r$[/tex], we can combine these implications.
- If [tex]$p$[/tex] is true, then [tex]$q$[/tex] must be true (from [tex]$p \Rightarrow q$[/tex]).
- Given [tex]$q$[/tex] is true, then [tex]$r$[/tex] must also be true (from [tex]$q \Rightarrow r$[/tex]).
3. Transitive Property:
- By the transitive property of implications, if [tex]$p$[/tex] leads to [tex]$q$[/tex] and [tex]$q$[/tex] leads to [tex]$r$[/tex], then [tex]$p$[/tex] must lead to [tex]$r$[/tex].
- Therefore, the combined implication is [tex]$p \Rightarrow r$[/tex].
Hence, the statement that must be true given [tex]$p \Rightarrow q$[/tex] and [tex]$q \Rightarrow r$[/tex] is:
[tex]\[ \boxed{p \Rightarrow r} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
