If you are given two traversal sequences, can you construct the binary tree?

It depends on what traversals are given. If one of the traversal methods is Inorder then the tree can be constructed, otherwise not.

Therefore, following combination can uniquely identify a tree.

• Inorder and Preorder. 
• Inorder and Postorder. 
• Inorder and Level-order. 

And following do not. 

• Postorder and Preorder. 
• Preorder and Level-order. 
• Postorder and Level-order. 

For example, Preorder, Level-order and Postorder traversals are same for the trees given in above diagram. 

• Preorder Traversal = AB 
• Postorder Traversal = BA 
• Level-Order Traversal = AB 

So, even if three of them (Pre, Post and Level) are given, the tree can not be constructed.