False propositions about events

High school · ●●○○○ 20 pts

Consider the following five propositions. ① Toss a coin twice. Let event

A

be "both tosses land heads" and event

B

be "both tosses land tails"; then

A

and

B

are complementary events. ② In proposition ①,

A

and

B

are mutually exclusive events. ③ Among 10 products, 3 are defective. Three products are selected at random. Let event

A

be "at most 2 of the selected products are defective" and event

B

be "at least 2 of the selected products are defective"; then

A

and

B

are mutually exclusive events. ④ If events

A

and

B

satisfy

P(A)+P(B)=1

, then

A

and

B

are complementary events. ⑤ If

A

and

B

are mutually exclusive events, then

\overline{A}\cup\overline{B}

is a certain event. Identify all the false propositions among these five and give their numbers, in increasing order.