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#### Please solve the problem below

Use your logic skills to derive the conclusion (A ↔ B) & E from the following assumptions.

J | L | Formula | Lines |
Rule | |||
---|---|---|---|---|---|---|---|

1 | A → B | A | |||||

2 | B → A | A | |||||

3 | E | A | |||||

4) | Lines |

- →
- ↔
- ∨
- &
- -
- (
- )

The following is a list of characters that can be used

- ✰ Any alphabetical character from A all the way to Z
- ✰ The conditional operator ( → ) can be inserted if you press the shift key and the > key at the same time
- ✰ The bi-conditional operator ( ↔ ) can be inserted if you press the shift key and the < key at the same time
- ✰ The disjunction operator ( ∨ ) can be inserted if you press the shift key and the v key at the same time
- ✰ The conjunction operator ( & ) can be inserted as you normally would type an ampersand
- ✰ The negation operator ( - ) can be inserted as you normally would type a dash
- ✰ Opening ( and closing ) parentheses can be inserted as you normally would type them
- ✰ Spaces!

The following list, though not exhaustive, cannot be entered

- ☹ Numerals ie 1234567890
- ☹ Punctuation like , . or even ?
- ☹ Brackets like { or [
- ☹ Probably some other stuff